diff --git a/info4/kapitel-0/Logik.ipynb b/info4/kapitel-0/Logik.ipynb
index 7ac1ca5af7d43b983235bd1c4788fc28aba3b593..4b4978fd637f5d1bad67fa3eff5bbe514179a232 100644
--- a/info4/kapitel-0/Logik.ipynb
+++ b/info4/kapitel-0/Logik.ipynb
@@ -12,7 +12,7 @@
"* Heinrich-Heine Universität Düsseldorf\n",
"\n",
"Grundlagen der Logik und Mengentheorie sind nicht im Skript.\n",
- "Hier definieren wir einige Grundlagen und Notationen die im Skript verwendet werden.\n",
+ "Hier definieren wir einige Grundlagen und Notationen, die im Skript verwendet werden.\n",
"Ein gutes Verständnis dieser Grundlagen und Notationen ist für das Verständnis des Skripts, aber auch anderer Teile der Informatik unumgänglich.\n",
"\n",
"Die Folien für diese Grundlagen sind als Jupyter Notebooks erstellt worden und im [Gitlab der Informatik](https://gitlab.cs.uni-duesseldorf.de/general/stups/prob-teaching-notebooks) erhältlich.\n"
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"<g id=\"edge11\" class=\"edge\">\n",
"<title>Node11->Node9</title>\n",
- "<path fill=\"none\" stroke=\"#000000\" d=\"M310.997,-35.0018C302.5314,-40.1752 293.0484,-45.9704 284.0611,-51.4627\"/>\n",
- "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"282.0027,-48.6187 275.295,-56.8197 285.6529,-54.5917 282.0027,-48.6187\"/>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M333.78,-34.7C325.39,-39.89 315.96,-45.71 307.01,-51.25\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"304.94,-48.41 298.27,-56.65 308.62,-54.37 304.94,-48.41\"/>\n",
"</g>\n",
"</g>\n",
"</svg>"
@@ -800,7 +800,7 @@
"\n",
"Man nennt so eine Interpretation ein <b>Modell</b> für die Formel.\n",
"\n",
- "* eine Interpretation $i$ so dass $i(\\phi)={\\color{olive} TRUE}$ ist ein <b>Modell</b> für $\\phi$\n",
+ "* eine Interpretation $i$ so dass $i(\\phi)={\\color{olive}{TRUE}}$ ist ein <b>Modell</b> für $\\phi$\n",
"* eine Formel $\\phi$ die mindestens ein Modell hat heißt <b>erfüllbar</b>\n",
"* eine Formel $\\phi$ wo alle Interpretationen auch Modelle sind wird eine <b>Tautologie</b> genannt\n",
"* eine Formel ohne Modell heißt <b>unerfüllbar</b> oder ein Widerspruch\n",
diff --git a/info4/kapitel-0/Mengentheorie.ipynb b/info4/kapitel-0/Mengentheorie.ipynb
index cd73a13428dc225e0be1c84c57601b035653c93b..327f7097067fc1ec4b644dddf357d7555396426a 100644
--- a/info4/kapitel-0/Mengentheorie.ipynb
+++ b/info4/kapitel-0/Mengentheorie.ipynb
@@ -5,15 +5,17 @@
"metadata": {},
"source": [
"# Theoretische Informatik - Vorlesung 0 - Teil 2 Mengentheorie\n",
- "April 2020\n",
- "Michael Leuschel\n",
- "Heinrich-Heine Universität Düsseldorf\n",
+ "\n",
+ "* April 2020\n",
+ "* Michael Leuschel\n",
+ "* Lehrstuhl Softwaretechnik und Programmiersprachen\n",
+ "* Heinrich-Heine Universität Düsseldorf\n",
"\n",
"Grundlagen der Logik und Mengentheorie sind nicht im Skript.\n",
"Hier definieren wir einige Grundlagen und Notationen die im Skript verwendet werden.\n",
"Ein gutes Verständnis dieser Grundlagen und Notationen ist für das Verständnis des Skripts, aber auch anderer Teile der Informatik unumgänglich.\n",
"\n",
- "Auswertung der Formeln erfolgt mit dem [Jupyter kernel](https://gitlab.cs.uni-duesseldorf.de/general/stups/prob2-jupyter-kernel) für [ProB](https://www3.hhu.de/stups/prob)\n",
+ "Auswertung der Formeln erfolgt mit dem [Jupyter Kernel](https://gitlab.cs.uni-duesseldorf.de/general/stups/prob2-jupyter-kernel) für [ProB](https://www3.hhu.de/stups/prob)\n",
"\n",
"\n",
"Um dieses Notebook zu starten kann man entweder selber Jupyter und den [ProB Kernel](https://gitlab.cs.uni-duesseldorf.de/general/stups/prob2-jupyter-kernel) installieren.\n",
@@ -62,13 +64,13 @@
"Sie hat keine Elemente:\n",
" * $z = \\emptyset \\Leftrightarrow \\forall(a).(a\\not\\in z)$\n",
"\n",
- "Zwei Mengen $x$ und $y$ sind gleich gdw wenn sie die gleichen Elemente haben:\n",
+ "Zwei Mengen $x$ und $y$ sind gleich gdw sie die gleichen Elemente haben:\n",
" * $\\forall(x,y).(x=y \\Leftrightarrow \\forall(a).(a\\in x \\Leftrightarrow a \\in y))$"
]
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -80,7 +82,7 @@
"FALSE"
]
},
- "execution_count": 17,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -91,7 +93,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -103,7 +105,7 @@
"FALSE"
]
},
- "execution_count": 18,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -114,7 +116,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -126,7 +128,7 @@
"TRUE"
]
},
- "execution_count": 19,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -147,7 +149,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -159,7 +161,7 @@
"TRUE"
]
},
- "execution_count": 20,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -177,7 +179,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -189,7 +191,7 @@
"FALSE"
]
},
- "execution_count": 22,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -200,7 +202,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -212,7 +214,7 @@
"FALSE"
]
},
- "execution_count": 23,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -230,7 +232,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -242,7 +244,7 @@
"TRUE"
]
},
- "execution_count": 24,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -271,7 +273,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -283,7 +285,7 @@
"{2,3,5,7}"
]
},
- "execution_count": 25,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -294,7 +296,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -306,7 +308,7 @@
"{5}"
]
},
- "execution_count": 26,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -317,7 +319,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -329,7 +331,7 @@
"{2,3}"
]
},
- "execution_count": 27,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -351,7 +353,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -363,7 +365,7 @@
"{2,3,5}"
]
},
- "execution_count": 28,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -381,7 +383,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -393,7 +395,7 @@
"{a∣a > 10}"
]
},
- "execution_count": 29,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -404,7 +406,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -416,7 +418,7 @@
"{2}"
]
},
- "execution_count": 30,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -438,7 +440,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -460,7 +462,7 @@
"\ty = {2,5}"
]
},
- "execution_count": 31,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -471,7 +473,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -493,7 +495,7 @@
"\ty = {2,5}"
]
},
- "execution_count": 32,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -504,7 +506,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -526,7 +528,7 @@
"\ty = {2,5}"
]
},
- "execution_count": 33,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -544,7 +546,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -556,7 +558,7 @@
"{1,2,3,4,5,6,7,8,9,10}"
]
},
- "execution_count": 34,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -579,7 +581,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -591,7 +593,7 @@
"{2,3,44,55}"
]
},
- "execution_count": 35,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -602,7 +604,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -614,7 +616,7 @@
"{2,3,44,55}"
]
},
- "execution_count": 36,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -668,7 +670,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -680,7 +682,7 @@
"{1,3,7,9}"
]
},
- "execution_count": 37,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -691,7 +693,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
@@ -703,7 +705,7 @@
"{1,3,5,7,9,10}"
]
},
- "execution_count": 38,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -714,7 +716,7 @@
},
{
"cell_type": "code",
- "execution_count": 39,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
@@ -726,7 +728,7 @@
"{1,2,3,4,6,7,8,9}"
]
},
- "execution_count": 39,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -737,7 +739,7 @@
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -749,7 +751,7 @@
"{1,3,7,9}"
]
},
- "execution_count": 40,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -779,9 +781,23 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 24,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\emptyset$"
+ ],
+ "text/plain": [
+ "∅"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"{2,4} ∩ (ℤ \\ {2,4})"
]
@@ -797,7 +813,7 @@
"* $\\forall a. a\\in x \\Rightarrow a \\in y$\n",
"\n",
"Wir benutzen diese Schreibweise $x \\subseteq y$.\n",
- "In diesem Fall ist $y$ auch eine Obermenge von $y$, geschrieben als $y \\supseteq x$.\n",
+ "In diesem Fall ist $y$ auch eine Obermenge von $x$, geschrieben als $y \\supseteq x$.\n",
"\n",
"Für die echte Teilmenge benutzen wir folgende Schreibweise und Definition:\n",
"* $x \\subset y$ $\\Leftrightarrow$ $(x \\subseteq y \\wedge x\\neq y)$."
@@ -805,7 +821,7 @@
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -825,7 +841,7 @@
"\ty = (1 ‥ 5)"
]
},
- "execution_count": 41,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -836,7 +852,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -848,7 +864,7 @@
"FALSE"
]
},
- "execution_count": 42,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -859,7 +875,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -871,7 +887,7 @@
"TRUE"
]
},
- "execution_count": 43,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -892,7 +908,7 @@
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -904,7 +920,7 @@
"3"
]
},
- "execution_count": 44,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -915,7 +931,7 @@
},
{
"cell_type": "code",
- "execution_count": 45,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -927,7 +943,7 @@
"3"
]
},
- "execution_count": 45,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -938,7 +954,7 @@
},
{
"cell_type": "code",
- "execution_count": 46,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -950,7 +966,7 @@
"0"
]
},
- "execution_count": 46,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -968,7 +984,7 @@
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -1015,7 +1031,7 @@
},
{
"cell_type": "code",
- "execution_count": 48,
+ "execution_count": 32,
"metadata": {},
"outputs": [
{
@@ -1047,7 +1063,7 @@
"\tO = 0"
]
},
- "execution_count": 48,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -1065,7 +1081,7 @@
},
{
"cell_type": "code",
- "execution_count": 49,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -1097,7 +1113,7 @@
"\tO = 3"
]
},
- "execution_count": 49,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@@ -1116,7 +1132,7 @@
},
{
"cell_type": "code",
- "execution_count": 50,
+ "execution_count": 34,
"metadata": {},
"outputs": [
{
@@ -1148,7 +1164,7 @@
"\tO = 4"
]
},
- "execution_count": 50,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -1167,7 +1183,7 @@
},
{
"cell_type": "code",
- "execution_count": 51,
+ "execution_count": 35,
"metadata": {},
"outputs": [
{
@@ -1199,7 +1215,7 @@
"\tO = 0"
]
},
- "execution_count": 51,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -1220,7 +1236,7 @@
},
{
"cell_type": "code",
- "execution_count": 52,
+ "execution_count": 36,
"metadata": {},
"outputs": [
{
@@ -1232,7 +1248,7 @@
"{(9↦5↦6↦7↦1↦0↦8↦2)}"
]
},
- "execution_count": 52,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -1248,7 +1264,7 @@
},
{
"cell_type": "code",
- "execution_count": 53,
+ "execution_count": 37,
"metadata": {},
"outputs": [
{
@@ -1263,7 +1279,7 @@
"9\t5\t6\t7\t1\t0\t8\t2\n"
]
},
- "execution_count": 53,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -1300,7 +1316,7 @@
},
{
"cell_type": "code",
- "execution_count": 54,
+ "execution_count": 38,
"metadata": {},
"outputs": [
{
@@ -1315,7 +1331,7 @@
"2\t0\t3\t4\t1\t8\t9\n"
]
},
- "execution_count": 54,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
@@ -1353,7 +1369,7 @@
},
{
"cell_type": "code",
- "execution_count": 55,
+ "execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1365,7 +1381,7 @@
"3"
]
},
- "execution_count": 55,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -1376,7 +1392,7 @@
},
{
"cell_type": "code",
- "execution_count": 56,
+ "execution_count": 40,
"metadata": {},
"outputs": [
{
@@ -1388,7 +1404,7 @@
"1"
]
},
- "execution_count": 56,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -1399,7 +1415,7 @@
},
{
"cell_type": "code",
- "execution_count": 57,
+ "execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -1411,7 +1427,7 @@
"2"
]
},
- "execution_count": 57,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
@@ -1422,7 +1438,7 @@
},
{
"cell_type": "code",
- "execution_count": 58,
+ "execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -1434,7 +1450,7 @@
"TRUE"
]
},
- "execution_count": 58,
+ "execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
@@ -1445,7 +1461,7 @@
},
{
"cell_type": "code",
- "execution_count": 59,
+ "execution_count": 43,
"metadata": {},
"outputs": [
{
@@ -1457,7 +1473,7 @@
"FALSE"
]
},
- "execution_count": 59,
+ "execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
@@ -1478,7 +1494,7 @@
},
{
"cell_type": "code",
- "execution_count": 60,
+ "execution_count": 44,
"metadata": {},
"outputs": [
{
@@ -1490,7 +1506,7 @@
"FALSE"
]
},
- "execution_count": 60,
+ "execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
@@ -1501,7 +1517,7 @@
},
{
"cell_type": "code",
- "execution_count": 61,
+ "execution_count": 45,
"metadata": {},
"outputs": [
{
@@ -1513,7 +1529,7 @@
"0"
]
},
- "execution_count": 61,
+ "execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
@@ -1524,7 +1540,7 @@
},
{
"cell_type": "code",
- "execution_count": 62,
+ "execution_count": 46,
"metadata": {},
"outputs": [
{
@@ -1536,7 +1552,7 @@
"1"
]
},
- "execution_count": 62,
+ "execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
@@ -1547,7 +1563,7 @@
},
{
"cell_type": "code",
- "execution_count": 63,
+ "execution_count": 47,
"metadata": {},
"outputs": [
{
@@ -1559,7 +1575,7 @@
"TRUE"
]
},
- "execution_count": 63,
+ "execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
@@ -1570,7 +1586,7 @@
},
{
"cell_type": "code",
- "execution_count": 64,
+ "execution_count": 48,
"metadata": {},
"outputs": [
{
@@ -1582,7 +1598,7 @@
"FALSE"
]
},
- "execution_count": 64,
+ "execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
@@ -1593,7 +1609,7 @@
},
{
"cell_type": "code",
- "execution_count": 65,
+ "execution_count": 49,
"metadata": {},
"outputs": [
{
@@ -1605,7 +1621,7 @@
"TRUE"
]
},
- "execution_count": 65,
+ "execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
@@ -1624,7 +1640,7 @@
},
{
"cell_type": "code",
- "execution_count": 66,
+ "execution_count": 50,
"metadata": {},
"outputs": [
{
@@ -1636,7 +1652,7 @@
"{∅,{1},{1,2},{2}}"
]
},
- "execution_count": 66,
+ "execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
@@ -1647,7 +1663,7 @@
},
{
"cell_type": "code",
- "execution_count": 67,
+ "execution_count": 51,
"metadata": {},
"outputs": [
{
@@ -1659,7 +1675,7 @@
"{∅}"
]
},
- "execution_count": 67,
+ "execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
@@ -1670,7 +1686,7 @@
},
{
"cell_type": "code",
- "execution_count": 68,
+ "execution_count": 52,
"metadata": {},
"outputs": [
{
@@ -1682,7 +1698,7 @@
"{∅,{1},{1,2},{1,3},{2},{1,2,3},{2,3},{3}}"
]
},
- "execution_count": 68,
+ "execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
@@ -1693,7 +1709,7 @@
},
{
"cell_type": "code",
- "execution_count": 69,
+ "execution_count": 53,
"metadata": {},
"outputs": [
{
@@ -1722,7 +1738,7 @@
"{3}\n"
]
},
- "execution_count": 69,
+ "execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
@@ -1733,7 +1749,7 @@
},
{
"cell_type": "code",
- "execution_count": 70,
+ "execution_count": 54,
"metadata": {},
"outputs": [
{
@@ -1754,7 +1770,7 @@
"{{1}}\n"
]
},
- "execution_count": 70,
+ "execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
@@ -1765,7 +1781,7 @@
},
{
"cell_type": "code",
- "execution_count": 71,
+ "execution_count": 55,
"metadata": {},
"outputs": [
{
@@ -1777,7 +1793,7 @@
"8"
]
},
- "execution_count": 71,
+ "execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
@@ -1788,7 +1804,7 @@
},
{
"cell_type": "code",
- "execution_count": 72,
+ "execution_count": 56,
"metadata": {},
"outputs": [
{
@@ -1800,7 +1816,7 @@
"1024"
]
},
- "execution_count": 72,
+ "execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
@@ -1811,7 +1827,7 @@
},
{
"cell_type": "code",
- "execution_count": 73,
+ "execution_count": 57,
"metadata": {},
"outputs": [
{
@@ -1823,7 +1839,7 @@
"1267650600228229401496703205376"
]
},
- "execution_count": 73,
+ "execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
@@ -1834,7 +1850,7 @@
},
{
"cell_type": "code",
- "execution_count": 74,
+ "execution_count": 58,
"metadata": {},
"outputs": [
{
@@ -1846,7 +1862,7 @@
"340282366920938463463374607431768211456"
]
},
- "execution_count": 74,
+ "execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
@@ -1857,7 +1873,7 @@
},
{
"cell_type": "code",
- "execution_count": 75,
+ "execution_count": 59,
"metadata": {},
"outputs": [
{
@@ -1869,7 +1885,7 @@
"115792089237316195423570985008687907853269984665640564039457584007913129639936"
]
},
- "execution_count": 75,
+ "execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
@@ -1915,7 +1931,7 @@
"## Relationen vs Prädikate\n",
"Eine Relation ist die explizite Darstellung eines Prädikats als Menge:\n",
" \n",
- "* Prädikate können mit logischen Junktoren und Quantoren verarabeitet werden:\n",
+ "* Prädikate können mit logischen Junktoren und Quantoren verarbeitet werden:\n",
" * $\\exists x. is\\_rich(x)$, $\\forall x.(is\\_poor(x) \\Rightarrow \\neg is\\_rich(x))$\n",
" \n",
"* Relationen können mit mengentheoretischen Operationen verarbeitet werden:\n",
@@ -1938,7 +1954,7 @@
},
{
"cell_type": "code",
- "execution_count": 78,
+ "execution_count": 60,
"metadata": {},
"outputs": [
{
@@ -1950,7 +1966,7 @@
"{(1↦4),(1↦5),(2↦4),(2↦5)}"
]
},
- "execution_count": 78,
+ "execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
@@ -1961,7 +1977,7 @@
},
{
"cell_type": "code",
- "execution_count": 79,
+ "execution_count": 61,
"metadata": {},
"outputs": [
{
@@ -1973,7 +1989,7 @@
"{(1↦4),(2↦4)}"
]
},
- "execution_count": 79,
+ "execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
@@ -1984,7 +2000,7 @@
},
{
"cell_type": "code",
- "execution_count": 80,
+ "execution_count": 62,
"metadata": {},
"outputs": [
{
@@ -1996,7 +2012,7 @@
"{(1↦FALSE),(1↦TRUE),(2↦FALSE),(2↦TRUE)}"
]
},
- "execution_count": 80,
+ "execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
@@ -2007,7 +2023,7 @@
},
{
"cell_type": "code",
- "execution_count": 81,
+ "execution_count": 63,
"metadata": {},
"outputs": [
{
@@ -2019,7 +2035,7 @@
"{(1↦1),(1↦2),(1↦3),(2↦1),(2↦2),(2↦3),(3↦1),(3↦2),(3↦3)}"
]
},
- "execution_count": 81,
+ "execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
@@ -2030,7 +2046,7 @@
},
{
"cell_type": "code",
- "execution_count": 82,
+ "execution_count": 64,
"metadata": {},
"outputs": [
{
@@ -2042,7 +2058,7 @@
"100"
]
},
- "execution_count": 82,
+ "execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
@@ -2060,7 +2076,7 @@
},
{
"cell_type": "code",
- "execution_count": 83,
+ "execution_count": 65,
"metadata": {},
"outputs": [
{
@@ -2072,7 +2088,7 @@
"{(2↦3)}"
]
},
- "execution_count": 83,
+ "execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
@@ -2083,7 +2099,7 @@
},
{
"cell_type": "code",
- "execution_count": 86,
+ "execution_count": 66,
"metadata": {},
"outputs": [
{
@@ -2095,7 +2111,7 @@
"{(3↦2)}"
]
},
- "execution_count": 86,
+ "execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
@@ -2126,7 +2142,7 @@
},
{
"cell_type": "code",
- "execution_count": 87,
+ "execution_count": 67,
"metadata": {},
"outputs": [
{
@@ -2138,7 +2154,7 @@
"{(0↦1),(0↦2),(0↦3),(0↦4),(0↦5),(0↦6),(0↦7),(0↦8),(0↦9),(1↦2),(1↦3),(1↦4),(1↦5),(1↦6),(1↦7),(1↦8),(1↦9),(2↦3),(2↦4),(2↦5),(2↦6),(2↦7),(2↦8),(2↦9),(3↦4),(3↦5),(3↦6),(3↦7),(3↦8),(3↦9),(4↦5),(4↦6),(4↦7),(4↦8),(4↦9),(5↦6),(5↦7),(5↦8),(5↦9),(6↦7),(6↦8),(6↦9),(7↦8),(7↦9),(8↦9)}"
]
},
- "execution_count": 87,
+ "execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
@@ -2157,7 +2173,7 @@
},
{
"cell_type": "code",
- "execution_count": 88,
+ "execution_count": 68,
"metadata": {},
"outputs": [
{
@@ -2169,7 +2185,7 @@
"{(2↦1),(4↦2),(6↦3),(8↦4),(10↦5)}"
]
},
- "execution_count": 88,
+ "execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
@@ -2187,7 +2203,7 @@
},
{
"cell_type": "code",
- "execution_count": 89,
+ "execution_count": 69,
"metadata": {},
"outputs": [
{
@@ -2196,83 +2212,96 @@
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@@ -2281,7 +2310,7 @@
"<Dot visualization: expr_as_graph [(\"halb\",{a,b|a:1..10 & b:1..10 & b*2=a})]>"
]
},
- "execution_count": 89,
+ "execution_count": 69,
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}
@@ -2300,7 +2329,7 @@
},
{
"cell_type": "code",
- "execution_count": 90,
+ "execution_count": 70,
"metadata": {},
"outputs": [
{
@@ -2312,7 +2341,7 @@
"{(1↦\"nein\"),(2↦\"nein\"),(3↦\"ja\"),(4↦\"nein\"),(5↦\"nein\"),(6↦\"ja\"),(7↦\"nein\")}"
]
},
- "execution_count": 90,
+ "execution_count": 70,
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}
@@ -2323,7 +2352,7 @@
},
{
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- "execution_count": 91,
+ "execution_count": 71,
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@@ -2434,7 +2479,7 @@
"<Dot visualization: expr_as_graph [(\"teilbar\",{x,y|x:1..7 & (x mod 3=0 => y=\"ja\") & (x mod 3>0 => y=\"nein\")})]>"
]
},
- "execution_count": 91,
+ "execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
@@ -2447,12 +2492,12 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Das Kartesische Produkt stellt die Relation dar die immer wahr ist (für die angegebenen Basismengen). Als Graph ist dies der [vollständige Graph](https://de.wikipedia.org/wiki/Vollständiger_Graph) über die Basismengen:"
+ "Das Kartesische Produkt stellt die Relation dar, die immer wahr ist (für die angegebenen Basismengen). Als Graph ist dies der [vollständige Graph](https://de.wikipedia.org/wiki/Vollständiger_Graph) über die Basismengen:"
]
},
{
"cell_type": "code",
- "execution_count": 92,
+ "execution_count": 72,
"metadata": {},
"outputs": [
{
@@ -2461,7 +2506,7 @@
"Preference changed: DOT_ENGINE = circo\n"
]
},
- "execution_count": 92,
+ "execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
@@ -2472,7 +2517,7 @@
},
{
"cell_type": "code",
- "execution_count": 93,
+ "execution_count": 73,
"metadata": {},
"outputs": [
{
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@@ -2671,7 +2746,7 @@
"<Dot visualization: expr_as_graph [(\"K5\",(1..5)*(1..5))]>"
]
},
- "execution_count": 93,
+ "execution_count": 73,
"metadata": {},
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}
@@ -2682,7 +2757,7 @@
},
{
"cell_type": "code",
- "execution_count": 94,
+ "execution_count": 74,
"metadata": {},
"outputs": [
{
@@ -2691,7 +2766,7 @@
"Preference changed: DOT_ENGINE = circo\n"
]
},
- "execution_count": 94,
+ "execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
@@ -2702,7 +2777,7 @@
},
{
"cell_type": "code",
- "execution_count": 95,
+ "execution_count": 75,
"metadata": {},
"outputs": [
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+ "<title>7->9</title>\n",
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+ "<title>7->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M92.49,-81.28C108.01,-71.41 127.23,-57.54 142.09,-45.53\"/>\n",
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+ "<g id=\"edge34\" class=\"edge\">\n",
+ "<title>7->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M92.54,-100.57C102.32,-100.71 110.3,-98.46 110.3,-93.82 110.3,-91 107.34,-89.06 102.81,-88.01\"/>\n",
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+ "<title>7->6</title>\n",
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+ "<g id=\"edge36\" class=\"edge\">\n",
+ "<title>7->5</title>\n",
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+ "<title>7->4</title>\n",
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+ "<g id=\"edge38\" class=\"edge\">\n",
+ "<title>7->3</title>\n",
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+ "<g id=\"edge39\" class=\"edge\">\n",
+ "<title>7->2</title>\n",
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+ "<g id=\"edge40\" class=\"edge\">\n",
+ "<title>7->1</title>\n",
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+ "<title>6->10</title>\n",
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+ "<title>6->9</title>\n",
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+ "<g id=\"edge43\" class=\"edge\">\n",
+ "<title>6->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M45.65,-193.51C73.96,-159.72 126.62,-87.39 151.77,-47.92\"/>\n",
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+ "<g id=\"edge44\" class=\"edge\">\n",
+ "<title>6->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M38.35,-193.57C46.53,-174.46 56.57,-144.15 62.19,-121.94\"/>\n",
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+ "<g id=\"edge45\" class=\"edge\">\n",
+ "<title>6->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.24,-218.44C64.02,-218.58 72,-216.34 72,-211.7 72,-208.87 69.04,-206.93 64.51,-205.88\"/>\n",
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+ "<g id=\"edge46\" class=\"edge\">\n",
+ "<title>6->5</title>\n",
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+ "<title>5->8</title>\n",
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+ "<title>5->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M69.11,-311.46C72.75,-270.66 73.01,-171.3 69.88,-122.22\"/>\n",
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+ "<g id=\"edge55\" class=\"edge\">\n",
+ "<title>5->6</title>\n",
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+ "<title>5->2</title>\n",
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+ "<g id=\"edge66\" class=\"edge\">\n",
+ "<title>4->5</title>\n",
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+ "<title>3->5</title>\n",
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+ "<title>3->1</title>\n",
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},
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+ "execution_count": 75,
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},
{
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- "execution_count": 96,
+ "execution_count": 76,
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.69,-48.78 331.14,-47.82 338.79,-55.15 341.69,-48.78\"/>\n",
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+ "<title>14</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"219.33,-112.6 165.33,-112.6 165.33,-76.6 219.33,-76.6 219.33,-112.6\"/>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"230.003,-99.6211 219.431,-100.316 228.129,-106.366 230.003,-99.6211\"/>\n",
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+ "<title>20->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M782.33,-283.11C683.43,-245.89 342.78,-135.09 229.37,-103.08\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"230,-99.62 219.43,-100.32 228.13,-106.37 230,-99.62\"/>\n",
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+ "<g id=\"node8\" class=\"node\">\n",
+ "<title>13</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"130.6,-201.33 76.6,-201.33 76.6,-165.33 130.6,-165.33 130.6,-201.33\"/>\n",
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- "<text text-anchor=\"middle\" x=\"460.659\" y=\"-243.772\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge8\" class=\"edge\">\n",
+ "<title>20->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M782.28,-287.95C673.1,-265.51 266.92,-201.04 141.04,-185.99\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"141.09,-182.48 130.76,-184.8 140.29,-189.43 141.09,-182.48\"/>\n",
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+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"73.63,-313.13 19.63,-313.13 19.63,-277.13 73.63,-277.13 73.63,-313.13\"/>\n",
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+ "<g id=\"edge9\" class=\"edge\">\n",
+ "<title>20->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M782.36,-292.42C666.97,-287.18 217.12,-287.04 83.96,-292\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"83.7,-288.51 73.85,-292.42 83.99,-295.5 83.7,-288.51\"/>\n",
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"</g>\n",
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- "<g id=\"node20\" class=\"node\"><title>11</title>\n",
+ "<g id=\"node10\" class=\"node\">\n",
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+ "<text text-anchor=\"middle\" x=\"27\" y=\"-415.37\" font-family=\"Times,serif\" font-size=\"14.00\">11</text>\n",
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- "<g id=\"edge20\" class=\"edge\"><title>20->11</title>\n",
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- "<text text-anchor=\"middle\" x=\"424.128\" y=\"-360.206\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge10\" class=\"edge\">\n",
+ "<title>20->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M782.16,-296.76C664.25,-310.08 199.36,-383.57 64.1,-410.05\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"63.33,-406.64 54.21,-412.02 64.7,-413.5 63.33,-406.64\"/>\n",
+ "<text text-anchor=\"middle\" x=\"408.63\" y=\"-342.21\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"node11\" class=\"node\">\n",
+ "<title>10</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"73.63,-561.01 19.63,-561.01 19.63,-525.01 73.63,-525.01 73.63,-561.01\"/>\n",
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+ "<g id=\"edge11\" class=\"edge\">\n",
+ "<title>20->10</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"82.1,-524.5 73.92,-531.24 84.52,-531.07 82.1,-524.5\"/>\n",
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+ "<g id=\"node12\" class=\"node\">\n",
+ "<title>9</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"130.6,-672.81 76.6,-672.81 76.6,-636.81 130.6,-636.81 130.6,-672.81\"/>\n",
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+ "<g id=\"edge12\" class=\"edge\">\n",
+ "<title>20->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M782.3,-305.91C672.7,-355.96 263.74,-564.15 139.56,-632.85\"/>\n",
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+ "<g id=\"node13\" class=\"node\">\n",
+ "<title>8</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"219.33,-761.54 165.33,-761.54 165.33,-725.54 219.33,-725.54 219.33,-761.54\"/>\n",
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+ "<title>20->8</title>\n",
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+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"331.13,-818.51 277.13,-818.51 277.13,-782.51 331.13,-782.51 331.13,-818.51\"/>\n",
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+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"455.07,-838.14 401.07,-838.14 401.07,-802.14 455.07,-802.14 455.07,-838.14\"/>\n",
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+ "<title>20->3</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"749.67,-626.26 752.26,-636.53 756.65,-626.89 749.67,-626.26\"/>\n",
+ "<text text-anchor=\"middle\" x=\"763.75\" y=\"-473.8\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<text text-anchor=\"middle\" x=\"809.511\" y=\"-538.808\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
+ "<g id=\"node19\" class=\"node\">\n",
+ "<title>2</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"836.51,-561.01 782.51,-561.01 782.51,-525.01 836.51,-525.01 836.51,-561.01\"/>\n",
+ "<text text-anchor=\"middle\" x=\"809.51\" y=\"-539.31\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
"</g>\n",
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- "<g id=\"edge38\" class=\"edge\"><title>20->2</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"801.541,-515.041 805.771,-524.754 808.522,-514.523 801.541,-515.041\"/>\n",
- "<text text-anchor=\"middle\" x=\"818.398\" y=\"-409.822\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge19\" class=\"edge\">\n",
+ "<title>20->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M805.77,-313.36C802.02,-356.16 801.78,-463.32 805.02,-514.68\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"801.54,-515.04 805.77,-524.75 808.52,-514.52 801.54,-515.04\"/>\n",
+ "<text text-anchor=\"middle\" x=\"790.9\" y=\"-402.82\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<text text-anchor=\"middle\" x=\"752.543\" y=\"-179.127\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "<g id=\"node20\" class=\"node\">\n",
+ "<title>1</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"779.54,-201.33 725.54,-201.33 725.54,-165.33 779.54,-165.33 779.54,-201.33\"/>\n",
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"</g>\n",
"<!-- 20->1 -->\n",
- "<g id=\"edge40\" class=\"edge\"><title>20->1</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"775.919,-208.239 767.796,-201.438 769.905,-211.82 775.919,-208.239\"/>\n",
- "<text text-anchor=\"middle\" x=\"775.326\" y=\"-245.28\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge20\" class=\"edge\">\n",
+ "<title>20->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M805.72,-276.89C798.71,-258.73 784.87,-230.73 772.94,-210.07\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"775.92,-208.24 767.8,-201.44 769.91,-211.82 775.92,-208.24\"/>\n",
+ "<text text-anchor=\"middle\" x=\"774.83\" y=\"-247.28\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 19->20 -->\n",
- "<g id=\"edge42\" class=\"edge\"><title>19->20</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"823.225,-322.288 817.493,-313.377 816.417,-323.917 823.225,-322.288\"/>\n",
- "<text text-anchor=\"middle\" x=\"811.517\" y=\"-359.821\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge21\" class=\"edge\">\n",
+ "<title>19->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M831.18,-400.81C830.11,-380.37 825.14,-347 819.85,-323.23\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"823.22,-322.29 817.49,-313.38 816.42,-323.92 823.22,-322.29\"/>\n",
+ "<text text-anchor=\"middle\" x=\"840.02\" y=\"-365.82\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 19->19 -->\n",
- "<g id=\"edge44\" class=\"edge\"><title>19->19</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M856.382,-425.814C866.165,-425.959 874.141,-423.711 874.141,-419.07 874.141,-416.243 871.179,-414.303 866.651,-413.252\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"866.655,-409.739 856.382,-412.327 866.027,-416.71 866.655,-409.739\"/>\n",
- "<text text-anchor=\"middle\" x=\"886.194\" y=\"-414.87\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge22\" class=\"edge\">\n",
+ "<title>19->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M856.38,-425.81C866.16,-425.96 874.14,-423.71 874.14,-419.07 874.14,-416.24 871.18,-414.3 866.65,-413.25\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"866.66,-409.74 856.38,-412.33 866.03,-416.71 866.66,-409.74\"/>\n",
+ "<text text-anchor=\"middle\" x=\"888.64\" y=\"-415.37\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 19->18 -->\n",
- "<g id=\"edge46\" class=\"edge\"><title>19->18</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M823.358,-400.618C800.502,-346.044 718.996,-185.482 682.007,-121.409\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"684.965,-119.534 676.885,-112.68 678.927,-123.076 684.965,-119.534\"/>\n",
- "<text text-anchor=\"middle\" x=\"766.683\" y=\"-249.814\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge23\" class=\"edge\">\n",
+ "<title>19->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M823.36,-400.62C800.5,-346.04 719,-185.48 682.01,-121.41\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"684.96,-119.53 676.89,-112.68 678.93,-123.08 684.96,-119.53\"/>\n",
+ "<text text-anchor=\"middle\" x=\"738.18\" y=\"-264.81\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge48\" class=\"edge\"><title>19->17</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M819.622,-400.945C780.578,-339.077 633.758,-136.54 575.701,-63.8446\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"578.081,-61.2207 569.074,-55.6412 572.636,-65.6195 578.081,-61.2207\"/>\n",
- "<text text-anchor=\"middle\" x=\"684.662\" y=\"-237.195\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge24\" class=\"edge\">\n",
+ "<title>19->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M819.62,-400.94C780.58,-339.08 633.76,-136.54 575.7,-63.84\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"578.08,-61.22 569.07,-55.64 572.64,-65.62 578.08,-61.22\"/>\n",
+ "<text text-anchor=\"middle\" x=\"683.16\" y=\"-236.19\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge50\" class=\"edge\"><title>19->16</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"460.429,-40.2923 450.691,-36.1203 455.702,-45.4549 460.429,-40.2923\"/>\n",
- "<text text-anchor=\"middle\" x=\"625.743\" y=\"-228.86\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge25\" class=\"edge\">\n",
+ "<title>19->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M814.95,-400.82C757.14,-336.08 539.45,-118.03 458.53,-43.3\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"460.43,-40.29 450.69,-36.12 455.7,-45.45 460.43,-40.29\"/>\n",
+ "<text text-anchor=\"middle\" x=\"622.24\" y=\"-225.86\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge52\" class=\"edge\"><title>19->15</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M809.282,-401.065C730.712,-337.894 441.394,-127.435 339.714,-59.1335\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.574,-56.1665 331.312,-53.5308 337.69,-61.9905 341.574,-56.1665\"/>\n",
- "<text text-anchor=\"middle\" x=\"582.498\" y=\"-213.899\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge26\" class=\"edge\">\n",
+ "<title>19->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M809.28,-401.07C730.71,-337.89 441.39,-127.44 339.71,-59.13\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.57,-56.17 331.31,-53.53 337.69,-61.99 341.57,-56.17\"/>\n",
+ "<text text-anchor=\"middle\" x=\"560\" y=\"-233.9\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 19->14 -->\n",
- "<g id=\"edge54\" class=\"edge\"><title>19->14</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"230.22,-106.286 219.672,-105.289 227.296,-112.646 230.22,-106.286\"/>\n",
- "<text text-anchor=\"middle\" x=\"509.373\" y=\"-263.458\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge27\" class=\"edge\">\n",
+ "<title>19->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M801.91,-401.81C700.43,-344.62 344.41,-163.12 228.84,-109.5\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"230.22,-106.29 219.67,-105.29 227.3,-112.65 230.22,-106.29\"/>\n",
+ "<text text-anchor=\"middle\" x=\"500.87\" y=\"-244.46\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge56\" class=\"edge\"><title>19->13</title>\n",
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- "<text text-anchor=\"middle\" x=\"475.282\" y=\"-283.461\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge28\" class=\"edge\">\n",
+ "<title>19->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M802.01,-407.3C690.64,-365.71 268.48,-228.42 140.55,-192.02\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"141.39,-188.62 130.82,-189.29 139.5,-195.36 141.39,-188.62\"/>\n",
+ "<text text-anchor=\"middle\" x=\"456.78\" y=\"-288.46\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge58\" class=\"edge\"><title>19->12</title>\n",
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- "<text text-anchor=\"middle\" x=\"441.877\" y=\"-361.76\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge29\" class=\"edge\">\n",
+ "<title>19->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M801.72,-411.98C683.78,-387.98 219.67,-314.35 84.04,-297.94\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"84.09,-294.42 73.76,-296.74 83.28,-301.38 84.09,-294.42\"/>\n",
+ "<text text-anchor=\"middle\" x=\"457.38\" y=\"-343.76\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge60\" class=\"edge\"><title>19->11</title>\n",
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+ "<g id=\"edge30\" class=\"edge\">\n",
+ "<title>19->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M801.99,-416.42C682.37,-411.09 202.14,-410.96 64.21,-416.01\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"63.99,-412.52 54.14,-416.42 64.27,-419.51 63.99,-412.52\"/>\n",
+ "<text text-anchor=\"middle\" x=\"418.6\" y=\"-420.02\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge62\" class=\"edge\"><title>19->10</title>\n",
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+ "<g id=\"edge31\" class=\"edge\">\n",
+ "<title>19->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M801.79,-420.7C683.88,-434.02 218.99,-507.5 83.73,-533.99\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"82.96,-530.57 73.84,-535.96 84.33,-537.44 82.96,-530.57\"/>\n",
+ "<text text-anchor=\"middle\" x=\"428.26\" y=\"-481.14\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge64\" class=\"edge\"><title>19->9</title>\n",
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- "<text text-anchor=\"middle\" x=\"474.332\" y=\"-539.997\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge32\" class=\"edge\">\n",
+ "<title>19->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M802.05,-425C690.74,-455.71 268.64,-592.69 140.62,-639.39\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"139.05,-636.24 130.88,-642.98 141.47,-642.81 139.05,-636.24\"/>\n",
+ "<text text-anchor=\"middle\" x=\"456.83\" y=\"-521\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge66\" class=\"edge\"><title>19->8</title>\n",
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+ "<g id=\"edge33\" class=\"edge\">\n",
+ "<title>19->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M802.08,-429.63C700.7,-475.69 343.48,-657.51 228.35,-721.37\"/>\n",
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+ "<g id=\"edge34\" class=\"edge\">\n",
+ "<title>19->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M801.99,-434.95C711.89,-494.52 423.64,-703.84 332.2,-775.97\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"329.88,-773.35 324.23,-782.32 334.23,-778.83 329.88,-773.35\"/>\n",
+ "<text text-anchor=\"middle\" x=\"552.6\" y=\"-594.26\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge35\" class=\"edge\">\n",
+ "<title>19->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M806.45,-437.26C735.37,-501.72 518.25,-718.74 449.27,-794.14\"/>\n",
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+ "<g id=\"edge36\" class=\"edge\">\n",
+ "<title>19->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M812.02,-437.15C761.64,-498.69 615.33,-699.87 567.33,-773.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"564.19,-771.77 561.72,-782.08 570.08,-775.56 564.19,-771.77\"/>\n",
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+ "<g id=\"edge37\" class=\"edge\">\n",
+ "<title>19->4</title>\n",
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+ "<g id=\"edge38\" class=\"edge\">\n",
+ "<title>19->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M819.15,-437.15C802.09,-478.05 769.49,-577.79 756.96,-626.77\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"753.51,-626.14 754.54,-636.69 760.31,-627.8 753.51,-626.14\"/>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"804.707,-514.621 807.464,-524.851 811.688,-515.135 804.707,-514.621\"/>\n",
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+ "<g id=\"edge39\" class=\"edge\">\n",
+ "<title>19->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M821.21,-437.11C815.91,-457.46 810.39,-490.81 808.21,-514.65\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"804.71,-514.62 807.46,-524.85 811.69,-515.13 804.71,-514.62\"/>\n",
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+ "<g id=\"edge40\" class=\"edge\">\n",
+ "<title>19->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M827.15,-400.97C817.74,-359.92 785.46,-259.6 766.33,-210.83\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"769.56,-209.48 762.58,-201.52 763.07,-212.1 769.56,-209.48\"/>\n",
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- "<text text-anchor=\"middle\" x=\"715.457\" y=\"-195.847\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge41\" class=\"edge\">\n",
+ "<title>18->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M672.35,-112.95C694.14,-148.8 751.21,-227.94 784.56,-269.14\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"782.04,-271.59 791.1,-277.09 787.45,-267.15 782.04,-271.59\"/>\n",
+ "<text text-anchor=\"middle\" x=\"713.96\" y=\"-179.85\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge84\" class=\"edge\"><title>18->19</title>\n",
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- "<text text-anchor=\"middle\" x=\"754.272\" y=\"-241.454\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge42\" class=\"edge\">\n",
+ "<title>18->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M669.6,-113.05C692.45,-167.62 773.96,-328.19 810.95,-392.26\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"807.99,-394.13 816.07,-400.99 814.03,-390.59 807.99,-394.13\"/>\n",
+ "<text text-anchor=\"middle\" x=\"725.77\" y=\"-241.45\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge86\" class=\"edge\"><title>18->18</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M691.055,-101.341C700.838,-101.486 708.814,-99.2383 708.814,-94.5976 708.814,-91.7698 705.852,-89.8304 701.324,-88.7796\"/>\n",
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+ "<g id=\"edge43\" class=\"edge\">\n",
+ "<title>18->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M691.05,-101.34C700.84,-101.49 708.81,-99.24 708.81,-94.6 708.81,-91.77 705.85,-89.83 701.32,-88.78\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"701.33,-85.27 691.05,-87.85 700.7,-92.24 701.33,-85.27\"/>\n",
+ "<text text-anchor=\"middle\" x=\"723.31\" y=\"-90.9\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge88\" class=\"edge\"><title>18->17</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"589.656,-45.8909 579.096,-45.0382 586.82,-52.2904 589.656,-45.8909\"/>\n",
- "<text text-anchor=\"middle\" x=\"608.722\" y=\"-70.6468\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge44\" class=\"edge\">\n",
+ "<title>18->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M641.06,-76.54C625.92,-67.55 605.72,-57.08 588.39,-49.16\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"589.66,-45.89 579.1,-45.04 586.82,-52.29 589.66,-45.89\"/>\n",
+ "<text text-anchor=\"middle\" x=\"600.22\" y=\"-51.65\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge90\" class=\"edge\"><title>18->16</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.646,-21.3059 455.085,-22.151 463.868,-28.0764 465.646,-21.3059\"/>\n",
- "<text text-anchor=\"middle\" x=\"546.897\" y=\"-60.6765\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge45\" class=\"edge\">\n",
+ "<title>18->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.79,-81C594.52,-64.37 512.68,-37.64 465,-24.76\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.65,-21.31 455.08,-22.15 463.87,-28.08 465.65,-21.31\"/>\n",
+ "<text text-anchor=\"middle\" x=\"536.4\" y=\"-56.68\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge92\" class=\"edge\"><title>18->15</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.771,-35.7178 331.46,-38.1554 341.04,-42.6796 341.771,-35.7178\"/>\n",
- "<text text-anchor=\"middle\" x=\"490.165\" y=\"-47.6371\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge46\" class=\"edge\">\n",
+ "<title>18->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.78,-86.46C573.24,-72.6 414.3,-47.26 341.55,-39.21\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.77,-35.72 331.46,-38.16 341.04,-42.68 341.77,-35.72\"/>\n",
+ "<text text-anchor=\"middle\" x=\"474.66\" y=\"-51.64\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge94\" class=\"edge\"><title>18->14</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.771,-91.2406C556.871,-86.8922 321.729,-86.7235 229.784,-90.7345\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"229.373,-87.2502 219.554,-91.2306 229.712,-94.242 229.373,-87.2502\"/>\n",
- "<text text-anchor=\"middle\" x=\"433.277\" y=\"-77.7875\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge47\" class=\"edge\">\n",
+ "<title>18->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.77,-91.24C556.87,-86.89 321.73,-86.72 229.78,-90.73\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"229.37,-87.25 219.55,-91.23 229.71,-94.24 229.37,-87.25\"/>\n",
+ "<text text-anchor=\"middle\" x=\"418.78\" y=\"-79.79\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge96\" class=\"edge\"><title>18->13</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.687,-95.7653C544.936,-105.535 246.111,-152.692 140.766,-173.795\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"139.996,-170.38 130.901,-175.814 141.4,-177.238 139.996,-170.38\"/>\n",
- "<text text-anchor=\"middle\" x=\"387.727\" y=\"-119.58\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge48\" class=\"edge\">\n",
+ "<title>18->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.69,-95.77C544.94,-105.54 246.11,-152.69 140.77,-173.8\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"140,-170.38 130.9,-175.81 141.4,-177.24 140,-170.38\"/>\n",
+ "<text text-anchor=\"middle\" x=\"374.23\" y=\"-123.58\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge98\" class=\"edge\"><title>18->12</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.782,-100.297C538.051,-127.218 196.892,-237.881 83.5516,-279.496\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"82.0809,-276.308 73.9249,-283.071 84.5178,-282.87 82.0809,-276.308\"/>\n",
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+ "<g id=\"edge49\" class=\"edge\">\n",
+ "<title>18->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.78,-100.3C538.05,-127.22 196.89,-237.88 83.55,-279.5\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"82.08,-276.31 73.92,-283.07 84.52,-282.87 82.08,-276.31\"/>\n",
+ "<text text-anchor=\"middle\" x=\"345.67\" y=\"-178.7\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge100\" class=\"edge\"><title>18->11</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"61.2365,-393.89 54.2147,-401.824 64.6515,-400.001 61.2365,-393.89\"/>\n",
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+ "<g id=\"edge50\" class=\"edge\">\n",
+ "<title>18->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.76,-105.16C535.37,-151.22 178.15,-333.04 63.03,-396.9\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"61.24,-393.89 54.21,-401.82 64.65,-400 61.24,-393.89\"/>\n",
+ "<text text-anchor=\"middle\" x=\"335.39\" y=\"-239.83\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge102\" class=\"edge\"><title>18->10</title>\n",
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+ "<g id=\"edge51\" class=\"edge\">\n",
+ "<title>18->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.77,-110.67C535.39,-178.07 178.82,-437.03 75.1,-518.45\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"72.63,-515.94 66.96,-524.89 76.98,-521.43 72.63,-515.94\"/>\n",
+ "<text text-anchor=\"middle\" x=\"341.43\" y=\"-303.36\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge104\" class=\"edge\"><title>18->9</title>\n",
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+ "<g id=\"edge52\" class=\"edge\">\n",
+ "<title>18->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M641.96,-112.62C552.32,-194.74 214.08,-532.88 125.1,-629.17\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"122.37,-626.97 118.2,-636.71 127.53,-631.7 122.37,-626.97\"/>\n",
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- "<g id=\"edge106\" class=\"edge\"><title>18->8</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"205.254,-715.026 202.678,-725.303 211.1,-718.875 205.254,-715.026\"/>\n",
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+ "<g id=\"edge53\" class=\"edge\">\n",
+ "<title>18->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M647.4,-112.89C574.32,-204.06 280.22,-608.69 208.21,-716.89\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"205.25,-715.03 202.68,-725.3 211.1,-718.88 205.25,-715.03\"/>\n",
+ "<text text-anchor=\"middle\" x=\"413.31\" y=\"-403.69\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge108\" class=\"edge\"><title>18->7</title>\n",
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+ "<g id=\"edge54\" class=\"edge\">\n",
+ "<title>18->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M651.87,-112.76C596.54,-208.84 367.77,-657.56 314.93,-773.26\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"311.68,-771.95 310.76,-782.51 318.06,-774.82 311.68,-771.95\"/>\n",
+ "<text text-anchor=\"middle\" x=\"468.9\" y=\"-431.81\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge55\" class=\"edge\">\n",
+ "<title>18->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M655.39,-112.9C617.55,-210.86 467.25,-672.98 434.27,-792.09\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"430.84,-791.35 431.61,-801.92 437.6,-793.18 430.84,-791.35\"/>\n",
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+ "<g id=\"edge56\" class=\"edge\">\n",
+ "<title>18->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M658.55,-112.75C637.61,-208.58 566.64,-655.66 553.58,-772.51\"/>\n",
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+ "<g id=\"edge57\" class=\"edge\">\n",
+ "<title>18->4</title>\n",
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+ "<g id=\"edge58\" class=\"edge\">\n",
+ "<title>18->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M664.08,-112.69C671.56,-194.19 724.14,-527.51 744.88,-626.79\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"741.48,-627.65 747.02,-636.68 748.33,-626.17 741.48,-627.65\"/>\n",
+ "<text text-anchor=\"middle\" x=\"689.98\" y=\"-373.54\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"793.662,-516.892 800.556,-524.938 800.184,-514.349 793.662,-516.892\"/>\n",
- "<text text-anchor=\"middle\" x=\"717.838\" y=\"-313.986\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge59\" class=\"edge\">\n",
+ "<title>18->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M666.76,-112.77C684.11,-182.37 765.01,-432.09 796.91,-515.6\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"793.66,-516.89 800.56,-524.94 800.18,-514.35 793.66,-516.89\"/>\n",
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- "<text text-anchor=\"middle\" x=\"707.694\" y=\"-120.456\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge60\" class=\"edge\">\n",
+ "<title>18->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M674.81,-112.9C685.81,-126.1 703.08,-143.94 718.58,-158.41\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"716.27,-161.04 726.01,-165.2 720.99,-155.87 716.27,-161.04\"/>\n",
+ "<text text-anchor=\"middle\" x=\"682.19\" y=\"-139.46\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"775.884,-272.683 785.645,-276.802 780.584,-267.495 775.884,-272.683\"/>\n",
- "<text text-anchor=\"middle\" x=\"660.677\" y=\"-169.663\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge61\" class=\"edge\">\n",
+ "<title>17->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M565.29,-55.79C604.77,-100.99 721.43,-218.11 778.07,-269.94\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"775.88,-272.68 785.65,-276.8 780.58,-267.49 775.88,-272.68\"/>\n",
+ "<text text-anchor=\"middle\" x=\"657.18\" y=\"-151.66\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge124\" class=\"edge\"><title>17->19</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"803.068,-395.48 812.075,-401.059 808.513,-391.081 803.068,-395.48\"/>\n",
- "<text text-anchor=\"middle\" x=\"696.487\" y=\"-211.106\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge62\" class=\"edge\">\n",
+ "<title>17->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M561.53,-55.76C600.57,-117.62 747.39,-320.16 805.45,-392.86\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"803.07,-395.48 812.07,-401.06 808.51,-391.08 803.07,-395.48\"/>\n",
+ "<text text-anchor=\"middle\" x=\"668.99\" y=\"-213.11\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge126\" class=\"edge\"><title>17->18</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.165,-86.3365 636.726,-87.1892 629.002,-79.9371 626.165,-86.3365\"/>\n",
- "<text text-anchor=\"middle\" x=\"607.1\" y=\"-53.1806\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge63\" class=\"edge\">\n",
+ "<title>17->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M574.76,-55.69C589.91,-64.67 610.1,-75.14 627.44,-83.07\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.17,-86.34 636.73,-87.19 629,-79.94 626.17,-86.34\"/>\n",
+ "<text text-anchor=\"middle\" x=\"586.6\" y=\"-73.18\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge128\" class=\"edge\"><title>17->17</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M579.249,-44.3732C589.032,-44.5182 597.008,-42.2704 597.008,-37.6298 597.008,-34.8019 594.046,-32.8626 589.519,-31.8118\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"589.523,-28.2981 579.249,-30.8864 588.894,-35.2698 589.523,-28.2981\"/>\n",
- "<text text-anchor=\"middle\" x=\"609.061\" y=\"-33.4298\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge64\" class=\"edge\">\n",
+ "<title>17->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M579.25,-44.37C589.03,-44.52 597.01,-42.27 597.01,-37.63 597.01,-34.8 594.05,-32.86 589.52,-31.81\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"589.52,-28.3 579.25,-30.89 588.89,-35.27 589.52,-28.3\"/>\n",
+ "<text text-anchor=\"middle\" x=\"611.51\" y=\"-33.93\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 17->16 -->\n",
- "<g id=\"edge130\" class=\"edge\"><title>17->16</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.786,-27.4856C507.369,-23.5665 484.545,-19.7996 465.442,-17.6307\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.572,-14.126 455.27,-16.5993 464.866,-21.0903 465.572,-14.126\"/>\n",
- "<text text-anchor=\"middle\" x=\"494.114\" y=\"-29.3581\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge65\" class=\"edge\">\n",
+ "<title>17->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.79,-27.49C507.37,-23.57 484.54,-19.8 465.44,-17.63\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.57,-14.13 455.27,-16.6 464.87,-21.09 465.57,-14.13\"/>\n",
+ "<text text-anchor=\"middle\" x=\"509.61\" y=\"-26.36\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge132\" class=\"edge\"><title>17->15</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.136,-29.1491 331.352,-33.2138 341.536,-36.1377 341.136,-29.1491\"/>\n",
- "<text text-anchor=\"middle\" x=\"433.001\" y=\"-19.7166\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge66\" class=\"edge\">\n",
+ "<title>17->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.53,-33.2C479.93,-30.31 391.72,-30.12 341.47,-32.64\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"341.14,-29.15 331.35,-33.21 341.54,-36.14 341.14,-29.15\"/>\n",
+ "<text text-anchor=\"middle\" x=\"447.5\" y=\"-36.72\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge134\" class=\"edge\"><title>17->14</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.975,-38.1265C461.447,-44.3424 302.554,-69.3007 229.784,-84.2568\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"228.755,-80.8969 219.693,-86.3875 230.201,-87.7458 228.755,-80.8969\"/>\n",
- "<text text-anchor=\"middle\" x=\"378.379\" y=\"-67.9917\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge67\" class=\"edge\">\n",
+ "<title>17->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.98,-38.13C461.45,-44.34 302.55,-69.3 229.78,-84.26\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"228.75,-80.9 219.69,-86.39 230.2,-87.75 228.75,-80.9\"/>\n",
+ "<text text-anchor=\"middle\" x=\"362.88\" y=\"-49.99\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge136\" class=\"edge\"><title>17->13</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.918,-42.8823C447.909,-63.3881 227.728,-134.724 140.153,-167.286\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"138.758,-164.071 130.635,-170.872 141.227,-170.621 138.758,-164.071\"/>\n",
- "<text text-anchor=\"middle\" x=\"335.536\" y=\"-112.884\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge68\" class=\"edge\">\n",
+ "<title>17->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.92,-42.88C447.91,-63.39 227.73,-134.72 140.15,-167.29\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"138.76,-164.07 130.63,-170.87 141.23,-170.62 138.76,-164.07\"/>\n",
+ "<text text-anchor=\"middle\" x=\"318.04\" y=\"-93.88\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge138\" class=\"edge\"><title>17->12</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.805,-47.914C439.729,-86.1556 178.846,-218.866 82.6871,-272.536\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"80.9051,-269.523 73.907,-277.478 84.3383,-275.623 80.9051,-269.523\"/>\n",
- "<text text-anchor=\"middle\" x=\"309.746\" y=\"-168.025\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge69\" class=\"edge\">\n",
+ "<title>17->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.8,-47.91C439.73,-86.16 178.85,-218.87 82.69,-272.54\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"80.91,-269.52 73.91,-277.48 84.34,-275.62 80.91,-269.52\"/>\n",
+ "<text text-anchor=\"middle\" x=\"289.25\" y=\"-149.03\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge140\" class=\"edge\"><title>17->11</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.858,-53.5117C434.757,-113.077 146.509,-322.4 55.0717,-394.53\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"52.7422,-391.911 47.0955,-400.875 57.1002,-397.389 52.7422,-391.911\"/>\n",
- "<text text-anchor=\"middle\" x=\"297.965\" y=\"-231.821\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge70\" class=\"edge\">\n",
+ "<title>17->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M524.86,-53.51C434.76,-113.08 146.51,-322.4 55.07,-394.53\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"52.74,-391.91 47.1,-400.88 57.1,-397.39 52.74,-391.91\"/>\n",
+ "<text text-anchor=\"middle\" x=\"275.46\" y=\"-212.82\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge142\" class=\"edge\"><title>17->10</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M529.867,-55.7353C446.139,-132.212 150.096,-428.161 67.8853,-517.433\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"65.1913,-515.193 61.0377,-524.939 70.3629,-519.91 65.1913,-515.193\"/>\n",
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+ "<g id=\"edge71\" class=\"edge\">\n",
+ "<title>17->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M529.87,-55.74C446.14,-132.21 150.1,-428.16 67.89,-517.43\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"65.19,-515.19 61.04,-524.94 70.36,-519.91 65.19,-515.19\"/>\n",
+ "<text text-anchor=\"middle\" x=\"284.38\" y=\"-290.38\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge144\" class=\"edge\"><title>17->9</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M535.502,-55.9439C464.742,-144.06 188.71,-523.826 119.377,-628.21\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"116.417,-626.341 113.852,-636.621 122.268,-630.184 116.417,-626.341\"/>\n",
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+ "<g id=\"edge72\" class=\"edge\">\n",
+ "<title>17->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M535.5,-55.94C464.74,-144.06 188.71,-523.83 119.38,-628.21\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"116.42,-626.34 113.85,-636.62 122.27,-630.18 116.42,-626.34\"/>\n",
+ "<text text-anchor=\"middle\" x=\"312.94\" y=\"-345.88\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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"<!-- 17->8 -->\n",
- "<g id=\"edge146\" class=\"edge\"><title>17->8</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"199.871,-714.984 198.959,-725.539 206.255,-717.857 199.871,-714.984\"/>\n",
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+ "<g id=\"edge73\" class=\"edge\">\n",
+ "<title>17->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M540.06,-55.79C484.73,-151.87 255.97,-600.59 203.12,-716.29\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"199.87,-714.98 198.96,-725.54 206.25,-717.86 199.87,-714.98\"/>\n",
+ "<text text-anchor=\"middle\" x=\"357.09\" y=\"-389.84\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge148\" class=\"edge\"><title>17->7</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"306.964,-771.731 307.719,-782.298 313.719,-773.566 306.964,-771.731\"/>\n",
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+ "<g id=\"edge74\" class=\"edge\">\n",
+ "<title>17->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M543.7,-55.78C504.79,-156.77 344.65,-649.16 310.39,-772.48\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"306.96,-771.73 307.72,-782.3 313.72,-773.57 306.96,-771.73\"/>\n",
+ "<text text-anchor=\"middle\" x=\"441.54\" y=\"-417.93\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge75\" class=\"edge\">\n",
+ "<title>17->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M546.84,-55.85C524.63,-158.72 444.02,-666.7 429.77,-792.11\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"426.29,-791.77 428.7,-802.08 433.25,-792.52 426.29,-791.77\"/>\n",
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+ "<g id=\"edge76\" class=\"edge\">\n",
+ "<title>17->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M549.76,-55.74C543.94,-156.49 543.76,-647.97 549.24,-772.03\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"545.75,-772.42 549.75,-782.24 552.74,-772.07 545.75,-772.42\"/>\n",
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+ "<g id=\"edge77\" class=\"edge\">\n",
+ "<title>17->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M552.54,-55.79C561.93,-151.66 632.55,-598.73 656.48,-715.55\"/>\n",
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+ "<g id=\"edge78\" class=\"edge\">\n",
+ "<title>17->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M555.36,-55.86C578.02,-143.48 700.53,-521.21 740.33,-627.12\"/>\n",
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+ "<g id=\"edge79\" class=\"edge\">\n",
+ "<title>17->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M558.23,-55.64C590.98,-131.47 740.13,-424.71 791.92,-515.85\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"789.02,-517.83 797.05,-524.75 795.09,-514.33 789.02,-517.83\"/>\n",
+ "<text text-anchor=\"middle\" x=\"660.58\" y=\"-289.54\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge80\" class=\"edge\">\n",
+ "<title>17->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M569.83,-55.86C602.82,-83.52 673.74,-135.4 716.91,-163.79\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"715.12,-166.8 725.42,-169.31 718.93,-160.93 715.12,-166.8\"/>\n",
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- "<g id=\"edge162\" class=\"edge\"><title>16->20</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"772.07,-277.21 782.344,-279.798 775.927,-271.368 772.07,-277.21\"/>\n",
- "<text text-anchor=\"middle\" x=\"602.577\" y=\"-162.939\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge81\" class=\"edge\">\n",
+ "<title>16->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M447.44,-36.18C508.13,-85.61 694.76,-221.5 773.71,-274.1\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"772.07,-277.21 782.34,-279.8 775.93,-271.37 772.07,-277.21\"/>\n",
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"</g>\n",
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- "<g id=\"edge164\" class=\"edge\"><title>16->19</title>\n",
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- "<text text-anchor=\"middle\" x=\"609.469\" y=\"-221.811\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge82\" class=\"edge\">\n",
+ "<title>16->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M442.26,-36.25C500.07,-100.99 717.76,-319.05 798.68,-393.77\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"796.78,-396.78 806.52,-400.95 801.51,-391.62 796.78,-396.78\"/>\n",
+ "<text text-anchor=\"middle\" x=\"605.97\" y=\"-203.81\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge166\" class=\"edge\"><title>16->18</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.238,-91.2917 636.8,-90.4466 628.017,-84.5213 626.238,-91.2917\"/>\n",
- "<text text-anchor=\"middle\" x=\"536.987\" y=\"-67.5211\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge83\" class=\"edge\">\n",
+ "<title>16->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M455.09,-31.6C497.37,-48.22 579.2,-74.95 626.88,-87.84\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.24,-91.29 636.8,-90.45 628.02,-84.52 626.24,-91.29\"/>\n",
+ "<text text-anchor=\"middle\" x=\"555.49\" y=\"-63.52\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge168\" class=\"edge\"><title>16->17</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.507,-41.5038 524.809,-39.0305 515.213,-34.5395 514.507,-41.5038\"/>\n",
- "<text text-anchor=\"middle\" x=\"485.965\" y=\"-17.8717\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge84\" class=\"edge\">\n",
+ "<title>16->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M455.29,-28.14C472.71,-32.06 495.53,-35.83 514.64,-38\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.51,-41.5 524.81,-39.03 515.21,-34.54 514.51,-41.5\"/>\n",
+ "<text text-anchor=\"middle\" x=\"499.46\" y=\"-36.87\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge170\" class=\"edge\"><title>16->16</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M455.311,-24.7434C465.094,-24.8884 473.07,-22.6406 473.07,-18 473.07,-15.1721 470.109,-13.2328 465.581,-12.182\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.585,-8.66827 455.311,-11.2566 464.957,-15.64 465.585,-8.66827\"/>\n",
- "<text text-anchor=\"middle\" x=\"485.124\" y=\"-13.8\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge85\" class=\"edge\">\n",
+ "<title>16->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M455.31,-24.74C465.09,-24.89 473.07,-22.64 473.07,-18 473.07,-15.17 470.11,-13.23 465.58,-12.18\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"465.59,-8.67 455.31,-11.26 464.96,-15.64 465.59,-8.67\"/>\n",
+ "<text text-anchor=\"middle\" x=\"487.57\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge172\" class=\"edge\"><title>16->15</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"340.257,-22.0202 331.202,-27.5201 341.711,-28.8677 340.257,-22.0202\"/>\n",
- "<text text-anchor=\"middle\" x=\"370.016\" y=\"-6.80495\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge86\" class=\"edge\">\n",
+ "<title>16->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M400.9,-16.6C383.37,-18.13 360.33,-21.57 341.13,-25.41\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"340.26,-22.02 331.2,-27.52 341.71,-28.87 340.26,-22.02\"/>\n",
+ "<text text-anchor=\"middle\" x=\"356.52\" y=\"-9.8\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge174\" class=\"edge\"><title>16->14</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M401.033,-22.157C358.704,-32.9008 276.755,-59.2693 229.101,-77.2458\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"227.557,-74.0897 219.48,-80.9458 230.07,-80.6232 227.557,-74.0897\"/>\n",
- "<text text-anchor=\"middle\" x=\"318.067\" y=\"-57.5014\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge87\" class=\"edge\">\n",
+ "<title>16->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M401.03,-22.16C358.7,-32.9 276.75,-59.27 229.1,-77.25\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"227.56,-74.09 219.48,-80.95 230.07,-80.62 227.56,-74.09\"/>\n",
+ "<text text-anchor=\"middle\" x=\"329.57\" y=\"-53.5\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge176\" class=\"edge\"><title>16->13</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M400.865,-27.5488C342.28,-53.3134 204.353,-123.343 139.04,-160.21\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"137.273,-157.189 130.322,-165.184 140.742,-163.269 137.273,-157.189\"/>\n",
- "<text text-anchor=\"middle\" x=\"275.952\" y=\"-101.68\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge88\" class=\"edge\">\n",
+ "<title>16->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M400.86,-27.55C342.28,-53.31 204.35,-123.34 139.04,-160.21\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"137.27,-157.19 130.32,-165.18 140.74,-163.27 137.27,-157.19\"/>\n",
+ "<text text-anchor=\"middle\" x=\"284.45\" y=\"-97.68\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"<!-- 16->12 -->\n",
- "<g id=\"edge178\" class=\"edge\"><title>16->12</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M400.951,-33.3037C330.814,-79.1137 144.29,-214.523 73.9419,-270.564\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"71.5496,-267.997 65.9544,-276.994 75.939,-273.45 71.5496,-267.997\"/>\n",
- "<text text-anchor=\"middle\" x=\"245.446\" y=\"-159.734\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge89\" class=\"edge\">\n",
+ "<title>16->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M400.95,-33.3C330.81,-79.11 144.29,-214.52 73.94,-270.56\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"71.55,-268 65.95,-276.99 75.94,-273.45 71.55,-268\"/>\n",
+ "<text text-anchor=\"middle\" x=\"222.95\" y=\"-140.73\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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"<!-- 16->11 -->\n",
- "<g id=\"edge180\" class=\"edge\"><title>16->11</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M405.377,-36.1872C334.299,-100.645 117.176,-317.67 48.197,-393.073\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"45.3761,-390.974 41.2611,-400.737 50.5663,-395.671 45.3761,-390.974\"/>\n",
- "<text text-anchor=\"middle\" x=\"237.787\" y=\"-221.43\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge90\" class=\"edge\">\n",
+ "<title>16->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M405.38,-36.19C334.3,-100.65 117.18,-317.67 48.2,-393.07\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"45.38,-390.97 41.26,-400.74 50.57,-395.67 45.38,-390.97\"/>\n",
+ "<text text-anchor=\"middle\" x=\"212.29\" y=\"-218.43\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge182\" class=\"edge\"><title>16->10</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M411.324,-36.298C347.873,-114.827 123.86,-422.986 62.2885,-516.196\"/>\n",
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+ "<g id=\"edge91\" class=\"edge\">\n",
+ "<title>16->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M411.32,-36.3C347.87,-114.83 123.86,-422.99 62.29,-516.2\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"59.22,-514.49 56.69,-524.78 65.09,-518.31 59.22,-514.49\"/>\n",
+ "<text text-anchor=\"middle\" x=\"222.31\" y=\"-280.05\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge184\" class=\"edge\"><title>16->9</title>\n",
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- "<text text-anchor=\"middle\" x=\"279.14\" y=\"-334.6\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge92\" class=\"edge\">\n",
+ "<title>16->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M415.93,-36.26C364.06,-125.93 163.46,-519.37 114.35,-627.34\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"111.09,-626.04 110.2,-636.6 117.48,-628.9 111.09,-626.04\"/>\n",
+ "<text text-anchor=\"middle\" x=\"250.64\" y=\"-335.6\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge186\" class=\"edge\"><title>16->8</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"195.096,-714.754 195.862,-725.321 201.853,-716.582 195.096,-714.754\"/>\n",
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+ "<g id=\"edge93\" class=\"edge\">\n",
+ "<title>16->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M419.64,-36.3C381.81,-134.27 231.51,-596.39 198.52,-715.49\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"195.1,-714.75 195.86,-725.32 201.85,-716.58 195.1,-714.75\"/>\n",
+ "<text text-anchor=\"middle\" x=\"294.58\" y=\"-379.7\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge188\" class=\"edge\"><title>16->7</title>\n",
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- "<text text-anchor=\"middle\" x=\"350.371\" y=\"-398.151\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge94\" class=\"edge\">\n",
+ "<title>16->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M422.91,-36.22C400.69,-139.09 320.09,-647.07 305.84,-772.48\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"302.35,-772.14 304.76,-782.45 309.31,-772.89 302.35,-772.14\"/>\n",
+ "<text text-anchor=\"middle\" x=\"349.87\" y=\"-408.15\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge190\" class=\"edge\"><title>16->6</title>\n",
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+ "<g id=\"edge95\" class=\"edge\">\n",
+ "<title>16->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M425.86,-36.26C419.98,-140.84 419.81,-663.54 425.36,-791.73\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"421.88,-792.09 425.86,-801.91 428.87,-791.75 421.88,-792.09\"/>\n",
+ "<text text-anchor=\"middle\" x=\"411.11\" y=\"-417.79\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge192\" class=\"edge\"><title>16->5</title>\n",
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+ "<g id=\"edge96\" class=\"edge\">\n",
+ "<title>16->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M428.71,-36.16C439.03,-138.87 519.31,-646.83 544.78,-772.4\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"541.39,-773.31 546.86,-782.39 548.25,-771.88 541.39,-773.31\"/>\n",
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+ "<g id=\"edge97\" class=\"edge\">\n",
+ "<title>16->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M431.62,-36.28C457.39,-134.27 607.6,-597.18 651.81,-715.8\"/>\n",
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+ "<g id=\"edge98\" class=\"edge\">\n",
+ "<title>16->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M434.63,-36.11C473.95,-125.64 674.89,-520.47 735.42,-627.81\"/>\n",
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+ "<g id=\"edge99\" class=\"edge\">\n",
+ "<title>16->2</title>\n",
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+ "<title>15->19</title>\n",
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+ "<title>15->18</title>\n",
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+ "<g id=\"edge104\" class=\"edge\">\n",
+ "<title>15->17</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"515,-46.11 524.79,-42.05 514.61,-39.12 515,-46.11\"/>\n",
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+ "<g id=\"edge105\" class=\"edge\">\n",
+ "<title>15->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.3,-39.03C348.84,-37.5 371.88,-34.06 391.08,-30.22\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"391.95,-33.61 401,-28.11 390.49,-26.76 391.95,-33.61\"/>\n",
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+ "<title>15->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.37,-44.37C341.16,-44.52 349.13,-42.27 349.13,-37.63 349.13,-34.8 346.17,-32.86 341.64,-31.81\"/>\n",
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+ "<title>15->14</title>\n",
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+ "<g id=\"edge108\" class=\"edge\">\n",
+ "<title>15->13</title>\n",
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+ "<title>15->12</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"39.1828,-390.333 36.7136,-400.636 45.0689,-394.122 39.1828,-390.333\"/>\n",
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+ "<title>15->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M287.01,-55.71C236.63,-117.25 90.33,-318.43 42.32,-391.93\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"39.18,-390.33 36.71,-400.64 45.07,-394.12 39.18,-390.33\"/>\n",
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+ "<title>15->10</title>\n",
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+ "<title>15->9</title>\n",
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+ "<title>15->8</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"190.42,-715.19 192.85,-725.5 197.38,-715.92 190.42,-715.19\"/>\n",
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+ "<title>15->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M301.88,-55.74C296.06,-156.49 295.89,-647.97 301.36,-772.03\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"297.88,-772.42 301.87,-782.24 304.87,-772.07 297.88,-772.42\"/>\n",
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+ "<title>15->6</title>\n",
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+ "<title>15->5</title>\n",
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+ "<g id=\"edge120\" class=\"edge\">\n",
+ "<title>15->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.44,-50.19C408.57,-79.67 628.05,-151.11 715.72,-175.43\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"714.93,-178.84 725.5,-178.09 716.77,-172.08 714.93,-178.84\"/>\n",
+ "<text text-anchor=\"middle\" x=\"509.08\" y=\"-116.61\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge242\" class=\"edge\"><title>14->20</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"771.836,-290.109 782.408,-289.414 773.71,-283.365 771.836,-290.109\"/>\n",
- "<text text-anchor=\"middle\" x=\"491.989\" y=\"-204.435\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge121\" class=\"edge\">\n",
+ "<title>14->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.51,-106.62C318.41,-143.84 659.06,-254.65 772.47,-286.65\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"771.84,-290.11 782.41,-289.41 773.71,-283.36 771.84,-290.11\"/>\n",
+ "<text text-anchor=\"middle\" x=\"481.49\" y=\"-200.44\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge244\" class=\"edge\"><title>14->19</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"791.248,-407.383 801.796,-408.379 794.172,-401.022 791.248,-407.383\"/>\n",
- "<text text-anchor=\"middle\" x=\"512.095\" y=\"-241.81\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge122\" class=\"edge\">\n",
+ "<title>14->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.56,-111.85C321.03,-169.04 677.06,-350.55 792.63,-404.17\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"791.25,-407.38 801.8,-408.38 794.17,-401.02 791.25,-407.38\"/>\n",
+ "<text text-anchor=\"middle\" x=\"491.59\" y=\"-261.81\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge246\" class=\"edge\"><title>14->18</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.768,-101.945 636.587,-97.9647 626.429,-94.9533 626.768,-101.945\"/>\n",
- "<text text-anchor=\"middle\" x=\"422.864\" y=\"-103.008\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge123\" class=\"edge\">\n",
+ "<title>14->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.37,-97.95C299.27,-102.3 534.41,-102.47 626.36,-98.46\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.77,-101.95 636.59,-97.96 626.43,-94.95 626.77,-101.95\"/>\n",
+ "<text text-anchor=\"middle\" x=\"408.36\" y=\"-102.01\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
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- "<g id=\"edge248\" class=\"edge\"><title>14->17</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"515.581,-51.3306 524.642,-45.84 514.134,-44.4816 515.581,-51.3306\"/>\n",
- "<text text-anchor=\"middle\" x=\"365.956\" y=\"-55.8357\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge124\" class=\"edge\">\n",
+ "<title>14->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.36,-94.1C282.89,-87.89 441.78,-62.93 514.55,-47.97\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"515.58,-51.33 524.64,-45.84 514.13,-44.48 515.58,-51.33\"/>\n",
+ "<text text-anchor=\"middle\" x=\"352.46\" y=\"-74.84\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge250\" class=\"edge\"><title>14->16</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"392.841,-38.508 400.918,-31.6519 390.328,-31.9744 392.841,-38.508\"/>\n",
- "<text text-anchor=\"middle\" x=\"308.331\" y=\"-70.6963\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge125\" class=\"edge\">\n",
+ "<title>14->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.36,-90.44C261.69,-79.7 343.64,-53.33 391.3,-35.35\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"392.84,-38.51 400.92,-31.65 390.33,-31.97 392.84,-38.51\"/>\n",
+ "<text text-anchor=\"middle\" x=\"290.83\" y=\"-66.7\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge252\" class=\"edge\"><title>14->15</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"274.191,-63.8673 281.113,-55.8464 270.7,-57.8 274.191,-63.8673\"/>\n",
- "<text text-anchor=\"middle\" x=\"239.853\" y=\"-57.8586\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge126\" class=\"edge\">\n",
+ "<title>14->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.45,-87.17C235.38,-80.36 255.57,-70.29 272.26,-60.94\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"274.19,-63.87 281.11,-55.85 270.7,-57.8 274.19,-63.87\"/>\n",
+ "<text text-anchor=\"middle\" x=\"260.35\" y=\"-77.86\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge254\" class=\"edge\"><title>14->14</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.568,-101.341C229.351,-101.486 237.327,-99.2383 237.327,-94.5976 237.327,-91.7698 234.365,-89.8304 229.838,-88.7796\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"229.842,-85.2659 219.568,-87.8542 229.213,-92.2377 229.842,-85.2659\"/>\n",
- "<text text-anchor=\"middle\" x=\"249.38\" y=\"-90.3976\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge127\" class=\"edge\">\n",
+ "<title>14->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.57,-101.34C229.35,-101.49 237.33,-99.24 237.33,-94.6 237.33,-91.77 234.37,-89.83 229.84,-88.78\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"229.84,-85.27 219.57,-87.85 229.21,-92.24 229.84,-85.27\"/>\n",
+ "<text text-anchor=\"middle\" x=\"251.83\" y=\"-90.9\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge256\" class=\"edge\"><title>14->13</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"118.424,-155.233 114.54,-165.09 123.723,-159.807 118.424,-155.233\"/>\n",
- "<text text-anchor=\"middle\" x=\"154.416\" y=\"-141.932\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge128\" class=\"edge\">\n",
+ "<title>14->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M165.73,-112.78C151.27,-125.7 133.87,-143.14 121.1,-157.48\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"118.42,-155.23 114.54,-165.09 123.72,-159.81 118.42,-155.23\"/>\n",
+ "<text text-anchor=\"middle\" x=\"128.92\" y=\"-138.93\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge258\" class=\"edge\"><title>14->12</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"57.2913,-266.77 54.9718,-277.108 63.2318,-270.473 57.2913,-266.77\"/>\n",
- "<text text-anchor=\"middle\" x=\"105.11\" y=\"-177.368\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge129\" class=\"edge\">\n",
+ "<title>14->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M173.8,-112.77C144.07,-148.31 86.87,-226.88 60.42,-268.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"57.29,-266.77 54.97,-277.11 63.23,-270.47 57.29,-266.77\"/>\n",
+ "<text text-anchor=\"middle\" x=\"131.61\" y=\"-194.37\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge260\" class=\"edge\"><title>14->11</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"33.4279,-390.276 32.6876,-400.845 39.8572,-393.045 33.4279,-390.276\"/>\n",
- "<text text-anchor=\"middle\" x=\"93.9809\" y=\"-240.865\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge130\" class=\"edge\">\n",
+ "<title>14->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M179.16,-112.84C146.82,-166.94 65.36,-326.5 36.8,-391.29\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"33.43,-390.28 32.69,-400.84 39.86,-393.04 33.43,-390.28\"/>\n",
+ "<text text-anchor=\"middle\" x=\"93.48\" y=\"-255.87\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge262\" class=\"edge\"><title>14->10</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M183.37,-112.672C155.682,-181.97 74.6371,-430.868 52.1266,-515.003\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"48.6909,-514.309 49.5682,-524.867 55.4667,-516.066 48.6909,-514.309\"/>\n",
- "<text text-anchor=\"middle\" x=\"103.748\" y=\"-305.638\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge131\" class=\"edge\">\n",
+ "<title>14->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M183.37,-112.67C155.68,-181.97 74.64,-430.87 52.13,-515\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"48.69,-514.31 49.57,-524.87 55.47,-516.07 48.69,-514.31\"/>\n",
+ "<text text-anchor=\"middle\" x=\"103.25\" y=\"-317.64\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"101.402,-626.247 103.879,-636.548 108.366,-626.95 101.402,-626.247\"/>\n",
- "<text text-anchor=\"middle\" x=\"159.844\" y=\"-367.378\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge132\" class=\"edge\">\n",
+ "<title>14->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M186.78,-112.83C168.47,-194.43 115.69,-526.55 104.91,-626.33\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"101.4,-626.25 103.88,-636.55 108.37,-626.95 101.4,-626.25\"/>\n",
+ "<text text-anchor=\"middle\" x=\"131.34\" y=\"-373.38\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge266\" class=\"edge\"><title>14->8</title>\n",
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+ "<g id=\"edge133\" class=\"edge\">\n",
+ "<title>14->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M189.91,-112.63C184.32,-202.77 184.14,-604.52 189.35,-715.22\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"185.86,-715.49 189.89,-725.29 192.85,-715.12 185.86,-715.49\"/>\n",
+ "<text text-anchor=\"middle\" x=\"175.13\" y=\"-417.73\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge268\" class=\"edge\"><title>14->7</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"293.407,-773.416 298.896,-782.478 300.256,-771.97 293.407,-773.416\"/>\n",
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+ "<g id=\"edge134\" class=\"edge\">\n",
+ "<title>14->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M192.86,-112.76C202.25,-208.63 272.87,-655.7 296.8,-772.52\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"293.41,-773.42 298.9,-782.48 300.26,-771.97 293.41,-773.42\"/>\n",
+ "<text text-anchor=\"middle\" x=\"230.33\" y=\"-446.44\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge270\" class=\"edge\"><title>14->6</title>\n",
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+ "<g id=\"edge135\" class=\"edge\">\n",
+ "<title>14->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M195.88,-112.88C221.64,-210.86 371.85,-673.77 416.07,-792.4\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"412.84,-793.77 419.66,-801.88 419.39,-791.29 412.84,-793.77\"/>\n",
+ "<text text-anchor=\"middle\" x=\"291.47\" y=\"-456.44\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"532.14,-775.495 540.123,-782.46 538.226,-772.036 532.14,-775.495\"/>\n",
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+ "<g id=\"edge136\" class=\"edge\">\n",
+ "<title>14->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M199.02,-112.73C241.51,-208.84 470.31,-658.3 535.06,-773.55\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"532.14,-775.49 540.12,-782.46 538.23,-772.04 532.14,-775.49\"/>\n",
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- "<g id=\"edge274\" class=\"edge\"><title>14->4</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"638.524,-719.696 647.482,-725.353 644.007,-715.344 638.524,-719.696\"/>\n",
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+ "<g id=\"edge137\" class=\"edge\">\n",
+ "<title>14->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M202.57,-112.66C261.55,-203.5 556.31,-609.54 641.07,-717.27\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"638.52,-719.7 647.48,-725.35 644.01,-715.34 638.52,-719.7\"/>\n",
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+ "<g id=\"edge138\" class=\"edge\">\n",
+ "<title>14->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M207.03,-112.82C281.91,-195.42 620.18,-533.99 722.91,-629.61\"/>\n",
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+ "<title>14->2</title>\n",
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+ "<g id=\"edge140\" class=\"edge\">\n",
+ "<title>14->1</title>\n",
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+ "<g id=\"edge141\" class=\"edge\">\n",
+ "<title>13->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.83,-190.51C240.01,-212.95 646.19,-277.42 772.07,-292.47\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"772.02,-295.98 782.35,-293.66 772.82,-289.03 772.02,-295.98\"/>\n",
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- "<text text-anchor=\"middle\" x=\"465.457\" y=\"-286.537\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge142\" class=\"edge\">\n",
+ "<title>13->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.73,-195.1C242.1,-236.69 664.26,-373.97 792.19,-410.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"791.35,-413.77 801.92,-413.11 793.24,-407.03 791.35,-413.77\"/>\n",
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+ "<g id=\"edge143\" class=\"edge\">\n",
+ "<title>13->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.72,-182.16C222.48,-172.39 521.3,-125.23 626.65,-104.13\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"627.42,-107.54 636.51,-102.11 626.01,-100.69 627.42,-107.54\"/>\n",
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- "<text text-anchor=\"middle\" x=\"320.07\" y=\"-99.6729\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge144\" class=\"edge\">\n",
+ "<title>13->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.69,-178.07C207.7,-157.57 427.88,-86.23 515.45,-53.67\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"516.85,-56.89 524.97,-50.08 514.38,-50.34 516.85,-56.89\"/>\n",
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- "<text text-anchor=\"middle\" x=\"255.716\" y=\"-91.2476\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge145\" class=\"edge\">\n",
+ "<title>13->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.8,-173.78C189.39,-148.01 327.32,-77.98 392.63,-41.12\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"394.4,-44.14 401.35,-36.14 390.93,-38.06 394.4,-44.14\"/>\n",
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+ "<g id=\"edge146\" class=\"edge\">\n",
+ "<title>13->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.9,-169.19C169.76,-144.36 240.35,-93.19 278.36,-62.41\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"280.89,-64.85 286.39,-55.8 276.45,-59.45 280.89,-64.85\"/>\n",
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- "<text text-anchor=\"middle\" x=\"163.509\" y=\"-149.593\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge147\" class=\"edge\">\n",
+ "<title>13->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.2,-165.15C144.65,-152.22 162.06,-134.79 174.82,-120.44\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"177.5,-122.69 181.38,-112.83 172.2,-118.12 177.5,-122.69\"/>\n",
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- "<g id=\"edge296\" class=\"edge\"><title>13->13</title>\n",
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+ "<g id=\"edge148\" class=\"edge\">\n",
+ "<title>13->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.84,-190.07C140.62,-190.22 148.6,-187.97 148.6,-183.33 148.6,-180.5 145.64,-178.56 141.11,-177.51\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"163.1\" y=\"-179.63\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge298\" class=\"edge\"><title>13->12</title>\n",
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- "<text text-anchor=\"middle\" x=\"57.3475\" y=\"-223.187\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge149\" class=\"edge\">\n",
+ "<title>13->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M88.37,-201.4C77.35,-219.26 63.2,-246.75 54.33,-267.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"50.99,-266.29 50.43,-276.87 57.46,-268.95 50.99,-266.29\"/>\n",
+ "<text text-anchor=\"middle\" x=\"56.85\" y=\"-238.19\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge300\" class=\"edge\"><title>13->11</title>\n",
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+ "<g id=\"edge150\" class=\"edge\">\n",
+ "<title>13->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M93.61,-201.41C76.55,-242.31 43.94,-342.05 31.41,-391.03\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"27.96,-390.4 28.99,-400.94 34.76,-392.06 27.96,-390.4\"/>\n",
+ "<text text-anchor=\"middle\" x=\"77.01\" y=\"-300.02\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"43.7605,-514.45 46.3416,-524.726 50.7319,-515.083 43.7605,-514.45\"/>\n",
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+ "<g id=\"edge151\" class=\"edge\">\n",
+ "<title>13->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M97.43,-201.65C83.58,-260.35 54.31,-443.91 47.25,-514.74\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"43.76,-514.45 46.34,-524.73 50.73,-515.08 43.76,-514.45\"/>\n",
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- "<g id=\"edge304\" class=\"edge\"><title>13->9</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"96.689,-626.904 100.788,-636.674 103.676,-626.48 96.689,-626.904\"/>\n",
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+ "<g id=\"edge152\" class=\"edge\">\n",
+ "<title>13->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M100.78,-201.52C95.74,-273.57 95.54,-539.22 100.18,-626.69\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"96.69,-626.9 100.79,-636.67 103.68,-626.48 96.69,-626.9\"/>\n",
+ "<text text-anchor=\"middle\" x=\"114.98\" y=\"-402.9\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge153\" class=\"edge\">\n",
+ "<title>13->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M103.86,-201.42C111.34,-282.92 163.93,-616.24 184.66,-715.52\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"181.27,-716.38 186.8,-725.41 188.11,-714.9 181.27,-716.38\"/>\n",
+ "<text text-anchor=\"middle\" x=\"129.76\" y=\"-462.27\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge154\" class=\"edge\">\n",
+ "<title>13->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M106.95,-201.56C129.61,-289.17 252.12,-666.91 291.92,-772.82\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"288.77,-774.38 295.61,-782.47 295.31,-771.88 288.77,-774.38\"/>\n",
+ "<text text-anchor=\"middle\" x=\"184.94\" y=\"-490.99\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge155\" class=\"edge\">\n",
+ "<title>13->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M110.16,-201.44C149.47,-290.96 350.42,-685.8 410.95,-793.14\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"408.04,-795.11 416.03,-802.06 414.12,-791.64 408.04,-795.11\"/>\n",
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+ "<g id=\"edge156\" class=\"edge\">\n",
+ "<title>13->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M113.88,-201.57C171.01,-289.69 447.63,-670.79 529.33,-774.44\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"526.79,-776.86 535.75,-782.51 532.27,-772.5 526.79,-776.86\"/>\n",
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+ "<g id=\"edge157\" class=\"edge\">\n",
+ "<title>13->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M118.3,-201.55C193.18,-284.15 531.45,-622.72 634.19,-718.34\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"632.01,-721.09 641.73,-725.31 636.76,-715.95 632.01,-721.09\"/>\n",
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+ "<g id=\"edge158\" class=\"edge\">\n",
+ "<title>13->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M124,-201.43C216.7,-275.29 598.23,-552.72 717.07,-633\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"715.23,-635.99 725.49,-638.66 719.13,-630.18 715.23,-635.99\"/>\n",
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+ "<g id=\"edge159\" class=\"edge\">\n",
+ "<title>13->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.84,-200.43C240.4,-261.96 648.74,-470.12 773.25,-528.06\"/>\n",
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+ "<g id=\"edge160\" class=\"edge\">\n",
+ "<title>13->1</title>\n",
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+ "<g id=\"edge161\" class=\"edge\">\n",
+ "<title>12->20</title>\n",
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+ "<g id=\"edge162\" class=\"edge\">\n",
+ "<title>12->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M74.06,-302.22C191.99,-326.23 656.1,-399.86 791.73,-416.26\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"791.68,-419.78 802.02,-417.47 792.49,-412.83 791.68,-419.78\"/>\n",
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- "<text text-anchor=\"middle\" x=\"347.277\" y=\"-183.634\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge163\" class=\"edge\">\n",
+ "<title>12->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.66,-289.43C172.39,-262.51 513.55,-151.85 626.89,-110.23\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"628.36,-113.42 636.52,-106.66 625.93,-106.86 628.36,-113.42\"/>\n",
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- "<text text-anchor=\"middle\" x=\"288.892\" y=\"-156.338\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge164\" class=\"edge\">\n",
+ "<title>12->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.83,-284.85C158.91,-246.61 419.79,-113.9 515.95,-60.23\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"517.73,-63.24 524.73,-55.29 514.3,-57.14 517.73,-63.24\"/>\n",
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- "<text text-anchor=\"middle\" x=\"245.254\" y=\"-168.999\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge165\" class=\"edge\">\n",
+ "<title>12->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.75,-279.83C143.89,-234.02 330.41,-98.61 400.76,-42.57\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"403.15,-45.14 408.75,-36.14 398.76,-39.68 403.15,-45.14\"/>\n",
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- "<g id=\"edge332\" class=\"edge\"><title>12->15</title>\n",
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- "<text text-anchor=\"middle\" x=\"166.265\" y=\"-154.93\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge166\" class=\"edge\">\n",
+ "<title>12->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M70.47,-276.83C120.88,-231.7 237.14,-115.51 284.06,-63.43\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"286.95,-65.45 290.98,-55.65 281.72,-60.8 286.95,-65.45\"/>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"181.666,-122.961 183.985,-112.623 175.725,-119.258 181.666,-122.961\"/>\n",
- "<text text-anchor=\"middle\" x=\"133.847\" y=\"-203.962\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge167\" class=\"edge\">\n",
+ "<title>12->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M65.16,-276.96C94.89,-241.42 152.08,-162.85 178.54,-121.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"181.67,-122.96 183.99,-112.62 175.73,-119.26 181.67,-122.96\"/>\n",
+ "<text text-anchor=\"middle\" x=\"107.35\" y=\"-202.96\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<text text-anchor=\"middle\" x=\"64.8799\" y=\"-232.873\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge168\" class=\"edge\">\n",
+ "<title>12->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M61.86,-277.06C72.88,-259.2 87.03,-231.71 95.9,-211.09\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"99.24,-212.17 99.8,-201.59 92.76,-209.51 99.24,-212.17\"/>\n",
+ "<text text-anchor=\"middle\" x=\"93.38\" y=\"-232.87\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"84.1443,-285.801 73.8706,-288.389 83.5161,-292.773 84.1443,-285.801\"/>\n",
- "<text text-anchor=\"middle\" x=\"103.683\" y=\"-290.933\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge169\" class=\"edge\">\n",
+ "<title>12->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.87,-301.88C83.65,-302.02 91.63,-299.77 91.63,-295.13 91.63,-292.3 88.67,-290.37 84.14,-289.31\"/>\n",
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+ "<g id=\"edge170\" class=\"edge\">\n",
+ "<title>12->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M38.7,-313.17C33.4,-333.52 27.88,-366.87 25.7,-390.71\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"22.2,-390.68 24.95,-400.91 29.18,-391.2 22.2,-390.68\"/>\n",
+ "<text text-anchor=\"middle\" x=\"17.7\" y=\"-355.74\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<text text-anchor=\"middle\" x=\"29.5171\" y=\"-409.822\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge171\" class=\"edge\">\n",
+ "<title>12->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M42.89,-313.36C39.14,-356.16 38.89,-463.32 42.14,-514.68\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"38.66,-515.04 42.89,-524.75 45.64,-514.52 38.66,-515.04\"/>\n",
+ "<text text-anchor=\"middle\" x=\"57.02\" y=\"-402.82\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge344\" class=\"edge\"><title>12->9</title>\n",
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+ "<g id=\"edge172\" class=\"edge\">\n",
+ "<title>12->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M46.33,-313.21C50.96,-371.61 79.82,-555.48 95.17,-626.46\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"91.82,-627.48 97.43,-636.47 98.65,-625.95 91.82,-627.48\"/>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"176.478,-717.428 183.372,-725.473 183,-714.885 176.478,-717.428\"/>\n",
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+ "<g id=\"edge173\" class=\"edge\">\n",
+ "<title>12->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M49.58,-313.31C66.93,-382.9 147.82,-632.63 179.73,-716.14\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"176.48,-717.43 183.37,-725.47 183,-714.88 176.48,-717.43\"/>\n",
+ "<text text-anchor=\"middle\" x=\"100.15\" y=\"-518.52\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge348\" class=\"edge\"><title>12->7</title>\n",
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+ "<g id=\"edge174\" class=\"edge\">\n",
+ "<title>12->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M52.85,-313.14C85.6,-388.97 234.75,-682.21 286.54,-773.35\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"283.64,-775.33 291.67,-782.25 289.71,-771.84 283.64,-775.33\"/>\n",
+ "<text text-anchor=\"middle\" x=\"155.2\" y=\"-547.05\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge175\" class=\"edge\">\n",
+ "<title>12->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M56.6,-313.22C106.93,-391.57 331.68,-701.3 404.98,-793.9\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"402.41,-796.3 411.39,-801.92 407.88,-791.93 402.41,-796.3\"/>\n",
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+ "<g id=\"edge176\" class=\"edge\">\n",
+ "<title>12->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M61.04,-313.21C130.09,-389.76 426.62,-686.62 522.23,-775.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"520.08,-778.15 529.81,-782.35 524.83,-773 520.08,-778.15\"/>\n",
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- "<g id=\"edge354\" class=\"edge\"><title>12->4</title>\n",
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+ "<g id=\"edge177\" class=\"edge\">\n",
+ "<title>12->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M67,-313.29C156.35,-384.61 513.73,-644.5 628.31,-721.8\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"626.5,-724.8 636.76,-727.46 630.4,-718.99 626.5,-724.8\"/>\n",
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+ "<g id=\"edge178\" class=\"edge\">\n",
+ "<title>12->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.87,-312.24C183.44,-373.76 591.77,-581.92 716.29,-639.87\"/>\n",
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+ "<g id=\"edge179\" class=\"edge\">\n",
+ "<title>12->2</title>\n",
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+ "<g id=\"edge180\" class=\"edge\">\n",
+ "<title>12->1</title>\n",
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+ "<g id=\"edge181\" class=\"edge\">\n",
+ "<title>11->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.35,-417.44C172.26,-404.12 637.15,-330.64 772.41,-304.15\"/>\n",
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+ "<g id=\"edge182\" class=\"edge\">\n",
+ "<title>11->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.15,-421.72C173.77,-427.05 654.01,-427.18 791.93,-422.13\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"792.15,-425.62 802,-421.72 791.87,-418.63 792.15,-425.62\"/>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"629.577,-119.778 636.599,-111.844 626.162,-113.667 629.577,-119.778\"/>\n",
- "<text text-anchor=\"middle\" x=\"334.923\" y=\"-246.439\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge183\" class=\"edge\">\n",
+ "<title>11->18</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.06,-408.51C155.44,-362.45 512.66,-180.63 627.79,-116.77\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"629.58,-119.78 636.6,-111.84 626.16,-113.67 629.58,-119.78\"/>\n",
+ "<text text-anchor=\"middle\" x=\"326.42\" y=\"-266.44\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"526.266,-64.7897 531.912,-55.825 521.908,-59.3117 526.266,-64.7897\"/>\n",
- "<text text-anchor=\"middle\" x=\"281.043\" y=\"-216.479\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge184\" class=\"edge\">\n",
+ "<title>11->17</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.15,-403.19C144.25,-343.62 432.5,-134.3 523.94,-62.17\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"526.27,-64.79 531.91,-55.82 521.91,-59.31 526.27,-64.79\"/>\n",
+ "<text text-anchor=\"middle\" x=\"274.54\" y=\"-236.48\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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"<!-- 11->16 -->\n",
- "<g id=\"edge370\" class=\"edge\"><title>11->16</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"409.694,-46.0969 413.809,-36.3338 404.504,-41.3998 409.694,-46.0969\"/>\n",
- "<text text-anchor=\"middle\" x=\"239.284\" y=\"-229.241\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge185\" class=\"edge\">\n",
+ "<title>11->16</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M49.69,-400.88C120.77,-336.43 337.89,-119.4 406.87,-44\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"409.69,-46.1 413.81,-36.33 404.5,-41.4 409.69,-46.1\"/>\n",
+ "<text text-anchor=\"middle\" x=\"242.78\" y=\"-226.24\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge372\" class=\"edge\"><title>11->15</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M44.1187,-400.995C94.5014,-339.45 240.806,-138.269 288.814,-64.7726\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"291.95,-66.367 294.419,-56.0639 286.064,-62.5784 291.95,-66.367\"/>\n",
- "<text text-anchor=\"middle\" x=\"153.466\" y=\"-219.684\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge186\" class=\"edge\">\n",
+ "<title>11->15</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M44.12,-401C94.5,-339.45 240.81,-138.27 288.81,-64.77\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"291.95,-66.37 294.42,-56.06 286.06,-62.58 291.95,-66.37\"/>\n",
+ "<text text-anchor=\"middle\" x=\"180.97\" y=\"-236.68\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge374\" class=\"edge\"><title>11->14</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"185.899,-123.392 186.64,-112.823 179.47,-120.624 185.899,-123.392\"/>\n",
- "<text text-anchor=\"middle\" x=\"97.3463\" y=\"-250.403\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge187\" class=\"edge\">\n",
+ "<title>11->14</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M40.17,-400.83C72.5,-346.73 153.96,-187.17 182.53,-122.38\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"185.9,-123.39 186.64,-112.82 179.47,-120.62 185.9,-123.39\"/>\n",
+ "<text text-anchor=\"middle\" x=\"125.85\" y=\"-265.4\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge376\" class=\"edge\"><title>11->13</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M36.9887,-400.987C54.0494,-360.092 86.6537,-260.347 99.1843,-211.371\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"102.634,-211.998 101.604,-201.453 95.8335,-210.338 102.634,-211.998\"/>\n",
- "<text text-anchor=\"middle\" x=\"82.0865\" y=\"-305.979\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge188\" class=\"edge\">\n",
+ "<title>11->13</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M36.99,-400.99C54.05,-360.09 86.65,-260.35 99.18,-211.37\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"102.63,-212 101.6,-201.45 95.83,-210.34 102.63,-212\"/>\n",
+ "<text text-anchor=\"middle\" x=\"53.59\" y=\"-309.98\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge378\" class=\"edge\"><title>11->12</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"51.434,-323.52 48.6771,-313.29 44.4529,-323.006 51.434,-323.52\"/>\n",
- "<text text-anchor=\"middle\" x=\"55.4278\" y=\"-360.062\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge189\" class=\"edge\">\n",
+ "<title>11->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M34.93,-401.03C40.23,-380.68 45.75,-347.33 47.93,-323.49\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"51.43,-323.52 48.68,-313.29 44.45,-323.01 51.43,-323.52\"/>\n",
+ "<text text-anchor=\"middle\" x=\"26.93\" y=\"-366.06\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge380\" class=\"edge\"><title>11->11</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"64.5146,-409.739 54.2408,-412.327 63.8863,-416.71 64.5146,-409.739\"/>\n",
- "<text text-anchor=\"middle\" x=\"84.0533\" y=\"-414.87\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge190\" class=\"edge\">\n",
+ "<title>11->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.24,-425.81C64.02,-425.96 72,-423.71 72,-419.07 72,-416.24 69.04,-414.3 64.51,-413.25\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"64.51,-409.74 54.24,-412.33 63.89,-416.71 64.51,-409.74\"/>\n",
+ "<text text-anchor=\"middle\" x=\"86.5\" y=\"-415.37\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge382\" class=\"edge\"><title>11->10</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"32.9163,-515.853 38.6476,-524.764 39.7241,-514.224 32.9163,-515.853\"/>\n",
- "<text text-anchor=\"middle\" x=\"44.6242\" y=\"-469.92\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge191\" class=\"edge\">\n",
+ "<title>11->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M24.96,-437.33C26.04,-457.77 31,-491.14 36.29,-514.91\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"32.92,-515.85 38.65,-524.76 39.72,-514.22 32.92,-515.85\"/>\n",
+ "<text text-anchor=\"middle\" x=\"16.12\" y=\"-479.92\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge384\" class=\"edge\"><title>11->9</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"86.5767,-628.656 93.5632,-636.621 93.0686,-626.038 86.5767,-628.656\"/>\n",
- "<text text-anchor=\"middle\" x=\"73.3975\" y=\"-524.04\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge192\" class=\"edge\">\n",
+ "<title>11->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M28.99,-437.17C38.4,-478.22 70.68,-578.54 89.81,-627.31\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"86.58,-628.66 93.56,-636.62 93.07,-626.04 86.58,-628.66\"/>\n",
+ "<text text-anchor=\"middle\" x=\"66.65\" y=\"-521.04\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge386\" class=\"edge\"><title>11->8</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M32.7825,-437.523C55.6388,-492.097 137.145,-652.659 174.134,-716.732\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"171.176,-718.607 179.256,-725.461 177.214,-715.065 171.176,-718.607\"/>\n",
- "<text text-anchor=\"middle\" x=\"89.4582\" y=\"-579.927\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
+ "<g id=\"edge193\" class=\"edge\">\n",
+ "<title>11->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M32.78,-437.52C55.64,-492.1 137.14,-652.66 174.13,-716.73\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"171.18,-718.61 179.26,-725.46 177.21,-715.06 171.18,-718.61\"/>\n",
+ "<text text-anchor=\"middle\" x=\"88.96\" y=\"-580.93\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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"<!-- 11->7 -->\n",
- "<g id=\"edge388\" class=\"edge\"><title>11->7</title>\n",
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+ "<g id=\"edge194\" class=\"edge\">\n",
+ "<title>11->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M36.52,-437.2C75.56,-499.06 222.38,-701.6 280.44,-774.3\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"278.06,-776.92 287.07,-782.5 283.51,-772.52 278.06,-776.92\"/>\n",
+ "<text text-anchor=\"middle\" x=\"143.98\" y=\"-609.55\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge390\" class=\"edge\"><title>11->6</title>\n",
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+ "<g id=\"edge195\" class=\"edge\">\n",
+ "<title>11->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M41.19,-437.32C99,-502.06 316.69,-720.12 397.61,-794.84\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"395.71,-797.85 405.45,-802.02 400.44,-792.69 395.71,-797.85\"/>\n",
+ "<text text-anchor=\"middle\" x=\"204.9\" y=\"-619.88\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge392\" class=\"edge\"><title>11->5</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M46.8589,-437.075C125.429,-500.247 414.747,-710.706 516.426,-779.007\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.567,-781.974 524.829,-784.61 518.451,-776.15 514.567,-781.974\"/>\n",
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+ "<g id=\"edge196\" class=\"edge\">\n",
+ "<title>11->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M46.86,-437.08C125.43,-500.25 414.75,-710.71 516.43,-779.01\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.57,-781.97 524.83,-784.61 518.45,-776.15 514.57,-781.97\"/>\n",
+ "<text text-anchor=\"middle\" x=\"267.14\" y=\"-611.84\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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- "<g id=\"edge394\" class=\"edge\"><title>11->4</title>\n",
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- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"625.921,-731.855 636.469,-732.851 628.845,-725.495 625.921,-731.855\"/>\n",
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+ "<g id=\"edge197\" class=\"edge\">\n",
+ "<title>11->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.23,-436.33C155.71,-493.52 511.73,-675.02 627.3,-728.64\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"625.92,-731.86 636.47,-732.85 628.84,-725.5 625.92,-731.86\"/>\n",
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- "<g id=\"edge396\" class=\"edge\"><title>11->3</title>\n",
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+ "<g id=\"edge198\" class=\"edge\">\n",
+ "<title>11->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.13,-430.84C165.5,-472.43 587.67,-609.72 715.59,-646.12\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"714.75,-649.52 725.32,-648.85 716.64,-642.78 714.75,-649.52\"/>\n",
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+ "<g id=\"edge199\" class=\"edge\">\n",
+ "<title>11->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.43,-426.16C172.36,-450.16 636.47,-523.8 772.1,-540.2\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"772.05,-543.72 782.39,-541.41 772.86,-536.77 772.05,-543.72\"/>\n",
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+ "<g id=\"edge200\" class=\"edge\">\n",
+ "<title>11->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.1,-413.14C165.4,-382.43 587.5,-245.45 715.52,-198.75\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"717.09,-201.9 725.26,-195.16 714.67,-195.33 717.09,-201.9\"/>\n",
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+ "<g id=\"edge201\" class=\"edge\">\n",
+ "<title>10->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.72,-537.02C189.1,-505.07 639.71,-358.83 772.5,-310.48\"/>\n",
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+ "<g id=\"edge202\" class=\"edge\">\n",
+ "<title>10->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.98,-541.38C191.89,-528.06 656.78,-454.58 792.04,-428.09\"/>\n",
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+ "<title>10->17</title>\n",
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+ "<title>10->15</title>\n",
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+ "<title>10->14</title>\n",
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+ "<g id=\"edge208\" class=\"edge\">\n",
+ "<title>10->13</title>\n",
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+ "<g id=\"edge209\" class=\"edge\">\n",
+ "<title>10->12</title>\n",
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+ "<g id=\"edge210\" class=\"edge\">\n",
+ "<title>10->11</title>\n",
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+ "<g id=\"edge211\" class=\"edge\">\n",
+ "<title>10->10</title>\n",
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+ "<title>10->9</title>\n",
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+ "<g id=\"edge213\" class=\"edge\">\n",
+ "<title>10->8</title>\n",
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+ "<title>10->7</title>\n",
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+ "<title>10->6</title>\n",
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+ "<title>10->5</title>\n",
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+ "<title>10->4</title>\n",
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+ "<g id=\"edge218\" class=\"edge\">\n",
+ "<title>10->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M73.86,-550.19C183.04,-572.63 589.22,-637.1 715.1,-652.15\"/>\n",
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+ "<title>10->2</title>\n",
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+ "<title>10->1</title>\n",
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+ "<title>9->20</title>\n",
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+ "<title>9->16</title>\n",
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+ "<title>9->15</title>\n",
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+ "<title>9->14</title>\n",
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+ "<title>9->13</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"110.51,-211.24 106.41,-201.47 103.52,-211.66 110.51,-211.24\"/>\n",
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+ "<g id=\"edge229\" class=\"edge\">\n",
+ "<title>9->12</title>\n",
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+ "<g id=\"edge230\" class=\"edge\">\n",
+ "<title>9->11</title>\n",
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+ "<g id=\"edge231\" class=\"edge\">\n",
+ "<title>9->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M99.8,-636.57C92.8,-618.41 78.95,-590.41 67.02,-569.75\"/>\n",
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+ "<g id=\"edge232\" class=\"edge\">\n",
+ "<title>9->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.84,-661.56C140.62,-661.7 148.6,-659.45 148.6,-654.81 148.6,-651.99 145.64,-650.05 141.11,-649\"/>\n",
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+ "<g id=\"edge233\" class=\"edge\">\n",
+ "<title>9->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M114.6,-673.12C125.6,-686.31 142.86,-704.16 158.36,-718.62\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"156.05,-721.26 165.79,-725.42 160.77,-716.09 156.05,-721.26\"/>\n",
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+ "<g id=\"edge234\" class=\"edge\">\n",
+ "<title>9->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M121.42,-673.04C154.41,-700.7 225.33,-752.59 268.5,-780.97\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"266.71,-783.99 277.01,-786.49 270.52,-778.11 266.71,-783.99\"/>\n",
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+ "<g id=\"edge235\" class=\"edge\">\n",
+ "<title>9->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.28,-672.93C188.23,-706.4 325.56,-776.5 391.52,-806.41\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"390.15,-809.64 400.71,-810.52 393.01,-803.25 390.15,-809.64\"/>\n",
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+ "<g id=\"edge236\" class=\"edge\">\n",
+ "<title>9->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.9,-667.37C208.03,-696.85 427.52,-768.29 515.19,-792.61\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.4,-796.02 524.96,-795.27 516.23,-789.27 514.4,-796.02\"/>\n",
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+ "<g id=\"edge237\" class=\"edge\">\n",
+ "<title>9->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.89,-662.32C222.79,-681.6 521.16,-728.99 626.54,-741.24\"/>\n",
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+ "<g id=\"edge238\" class=\"edge\">\n",
+ "<title>9->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.66,-657.73C233.11,-662.69 597.39,-662.84 715.37,-658.17\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"715.53,-661.67 725.37,-657.73 715.23,-654.67 715.53,-661.67\"/>\n",
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- "<g id=\"edge478\" class=\"edge\"><title>9->2</title>\n",
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+ "<g id=\"edge239\" class=\"edge\">\n",
+ "<title>9->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.85,-653.33C240.16,-641.2 647.03,-576.91 772.46,-552.17\"/>\n",
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+ "<g id=\"edge240\" class=\"edge\">\n",
+ "<title>9->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M130.7,-638.62C235.94,-568.52 616.57,-292.07 724.1,-207.78\"/>\n",
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+ "<g id=\"edge241\" class=\"edge\">\n",
+ "<title>8->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.37,-727.47C320.75,-660.07 677.32,-401.11 781.04,-319.69\"/>\n",
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+ "<title>8->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.38,-732.98C320.77,-686.92 677.99,-505.1 793.12,-441.24\"/>\n",
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+ "<title>8->18</title>\n",
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+ "<title>8->17</title>\n",
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+ "<title>8->16</title>\n",
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+ "<title>8->14</title>\n",
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+ "<title>8->13</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"114.66,-210.49 109.13,-201.46 107.81,-211.97 114.66,-210.49\"/>\n",
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+ "<title>8->12</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M189.38,-725.37C172.03,-655.77 91.13,-406.05 59.23,-322.54\"/>\n",
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+ "<g id=\"edge250\" class=\"edge\">\n",
+ "<title>8->11</title>\n",
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+ "<g id=\"edge251\" class=\"edge\">\n",
+ "<title>8->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M183.79,-725.19C162,-689.34 104.93,-610.2 71.58,-569\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"74.1,-566.55 65.04,-561.05 68.69,-570.99 74.1,-566.55\"/>\n",
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+ "<g id=\"edge252\" class=\"edge\">\n",
+ "<title>8->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M181.33,-725.24C170.33,-712.04 153.07,-694.2 137.57,-679.73\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"139.87,-677.1 130.13,-672.94 135.15,-682.27 139.87,-677.1\"/>\n",
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+ "<g id=\"edge253\" class=\"edge\">\n",
+ "<title>8->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.57,-750.29C229.35,-750.43 237.33,-748.18 237.33,-743.54 237.33,-740.72 234.37,-738.78 229.84,-737.73\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"251.83\" y=\"-739.84\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
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+ "<g id=\"edge254\" class=\"edge\">\n",
+ "<title>8->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M215.08,-761.6C230.23,-770.59 250.42,-781.06 267.76,-788.99\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"266.48,-792.25 277.04,-793.1 269.32,-785.85 266.48,-792.25\"/>\n",
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+ "<g id=\"edge255\" class=\"edge\">\n",
+ "<title>8->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.35,-757.14C261.62,-773.77 343.46,-800.5 391.14,-813.39\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"390.5,-816.83 401.06,-815.99 392.27,-810.06 390.5,-816.83\"/>\n",
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+ "<g id=\"edge256\" class=\"edge\">\n",
+ "<title>8->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.36,-751.68C282.9,-765.55 441.84,-790.88 514.59,-798.93\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"514.37,-802.42 524.68,-799.99 515.1,-795.46 514.37,-802.42\"/>\n",
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+ "<g id=\"edge257\" class=\"edge\">\n",
+ "<title>8->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.37,-746.9C299.27,-751.25 534.41,-751.42 626.36,-747.41\"/>\n",
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+ "<g id=\"edge258\" class=\"edge\">\n",
+ "<title>8->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.45,-742.38C311.2,-732.61 610.03,-685.45 715.37,-664.35\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"716.15,-667.76 725.24,-662.33 714.74,-660.9 716.15,-667.76\"/>\n",
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+ "<g id=\"edge259\" class=\"edge\">\n",
+ "<title>8->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M219.36,-737.84C318.09,-710.92 659.25,-600.26 772.59,-558.65\"/>\n",
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+ "<g id=\"edge260\" class=\"edge\">\n",
+ "<title>8->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M214.18,-725.52C303.82,-643.4 642.06,-305.26 731.04,-208.97\"/>\n",
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+ "<g id=\"edge261\" class=\"edge\">\n",
+ "<title>7->20</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"790.95,-322.95 795.1,-313.2 785.78,-318.23 790.95,-322.95\"/>\n",
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+ "<title>7->19</title>\n",
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+ "<title>7->18</title>\n",
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+ "<title>7->15</title>\n",
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+ "<g id=\"edge267\" class=\"edge\">\n",
+ "<title>7->14</title>\n",
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+ "<g id=\"edge268\" class=\"edge\">\n",
+ "<title>7->13</title>\n",
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+ "<g id=\"edge269\" class=\"edge\">\n",
+ "<title>7->12</title>\n",
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+ "<g id=\"edge270\" class=\"edge\">\n",
+ "<title>7->11</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M294.61,-782.39C255.57,-720.52 108.75,-517.98 50.69,-445.29\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"53.07,-442.66 44.07,-437.08 47.63,-447.06 53.07,-442.66\"/>\n",
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+ "<g id=\"edge271\" class=\"edge\">\n",
+ "<title>7->10</title>\n",
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+ "<g id=\"edge272\" class=\"edge\">\n",
+ "<title>7->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M286.31,-782.28C253.32,-754.62 182.4,-702.74 139.23,-674.35\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"141.02,-671.34 130.72,-668.83 137.21,-677.21 141.02,-671.34\"/>\n",
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+ "<g id=\"edge273\" class=\"edge\">\n",
+ "<title>7->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M281.38,-782.45C266.23,-773.47 246.04,-763 228.7,-755.07\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"229.98,-751.8 219.42,-750.95 227.14,-758.2 229.98,-751.8\"/>\n",
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+ "<g id=\"edge274\" class=\"edge\">\n",
+ "<title>7->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.37,-807.25C341.16,-807.4 349.13,-805.15 349.13,-800.51 349.13,-797.68 346.17,-795.74 341.64,-794.69\"/>\n",
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+ "<g id=\"edge275\" class=\"edge\">\n",
+ "<title>7->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.36,-810.66C348.77,-814.57 371.6,-818.34 390.7,-820.51\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"390.57,-824.01 400.87,-821.54 391.28,-817.05 390.57,-824.01\"/>\n",
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+ "<g id=\"edge276\" class=\"edge\">\n",
+ "<title>7->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.61,-804.94C376.21,-807.83 464.42,-808.02 514.67,-805.5\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"515,-808.99 524.79,-804.93 514.61,-802 515,-808.99\"/>\n",
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+ "<g id=\"edge277\" class=\"edge\">\n",
+ "<title>7->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.17,-800.01C394.69,-793.8 553.59,-768.84 626.36,-753.88\"/>\n",
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+ "<g id=\"edge278\" class=\"edge\">\n",
+ "<title>7->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.22,-795.26C408.23,-774.75 628.41,-703.42 715.99,-670.86\"/>\n",
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+ "<g id=\"edge279\" class=\"edge\">\n",
+ "<title>7->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M331.34,-790.23C416.41,-751.99 677.3,-619.27 773.45,-565.6\"/>\n",
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+ "<g id=\"edge280\" class=\"edge\">\n",
+ "<title>7->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M320.64,-782.2C391.4,-694.08 667.43,-314.31 736.76,-209.93\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"739.72,-211.8 742.29,-201.52 733.87,-207.96 739.72,-211.8\"/>\n",
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+ "<g id=\"edge281\" class=\"edge\">\n",
+ "<title>6->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M444.82,-801.84C508.27,-723.31 732.28,-415.15 793.85,-321.95\"/>\n",
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+ "<g id=\"edge282\" class=\"edge\">\n",
+ "<title>6->19</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M450.76,-801.95C521.84,-737.5 738.96,-520.47 807.94,-445.07\"/>\n",
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+ "<title>6->18</title>\n",
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+ "<title>6->10</title>\n",
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+ "<title>6->8</title>\n",
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+ "<g id=\"edge294\" class=\"edge\">\n",
+ "<title>6->7</title>\n",
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+ "<g id=\"edge295\" class=\"edge\">\n",
+ "<title>6->6</title>\n",
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+ "<g id=\"edge296\" class=\"edge\">\n",
+ "<title>6->5</title>\n",
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+ "<title>6->3</title>\n",
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+ "<title>6->2</title>\n",
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+ "<title>6->1</title>\n",
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+ "<title>4->13</title>\n",
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+ "<title>4->12</title>\n",
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+ "<title>4->11</title>\n",
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+ "<g id=\"edge331\" class=\"edge\">\n",
+ "<title>4->10</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.63,-731.52C537.73,-694.3 197.08,-583.5 83.68,-551.49\"/>\n",
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+ "<g id=\"edge332\" class=\"edge\">\n",
+ "<title>4->9</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.53,-736.03C544.62,-716.76 246.25,-669.36 140.87,-657.12\"/>\n",
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+ "<g id=\"edge333\" class=\"edge\">\n",
+ "<title>4->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.77,-740.19C556.87,-735.84 321.73,-735.67 229.78,-739.68\"/>\n",
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+ "<g id=\"edge334\" class=\"edge\">\n",
+ "<title>4->7</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"340.56,-786.81 331.5,-792.3 342.01,-793.66 340.56,-786.81\"/>\n",
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+ "<g id=\"edge335\" class=\"edge\">\n",
+ "<title>4->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.78,-747.7C594.45,-758.44 512.5,-784.81 464.84,-802.79\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"463.3,-799.63 455.22,-806.49 465.81,-806.17 463.3,-799.63\"/>\n",
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+ "<g id=\"edge336\" class=\"edge\">\n",
+ "<title>4->5</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M636.69,-750.97C620.76,-757.78 600.57,-767.85 583.89,-777.2\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"581.95,-774.27 575.03,-782.29 585.44,-780.34 581.95,-774.27\"/>\n",
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+ "<g id=\"edge337\" class=\"edge\">\n",
+ "<title>4->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M691.05,-750.29C700.84,-750.43 708.81,-748.18 708.81,-743.54 708.81,-740.72 705.85,-738.78 701.32,-737.73\"/>\n",
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+ "<g id=\"edge338\" class=\"edge\">\n",
+ "<title>4->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M690.41,-725.36C704.87,-712.44 722.27,-695 735.04,-680.66\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"737.72,-682.91 741.6,-673.05 732.42,-678.33 737.72,-682.91\"/>\n",
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+ "<g id=\"edge339\" class=\"edge\">\n",
+ "<title>4->2</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M682.34,-725.37C712.07,-689.83 769.27,-611.26 795.72,-569.78\"/>\n",
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+ "<title>4->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M669.36,-725.32C687.67,-643.71 740.45,-311.59 751.23,-211.81\"/>\n",
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+ "<g id=\"edge341\" class=\"edge\">\n",
+ "<title>3->20</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M758.71,-636.49C772.56,-577.8 801.83,-394.23 808.89,-323.4\"/>\n",
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+ "<title>3->19</title>\n",
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+ "<title>3->10</title>\n",
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+ "<g id=\"edge353\" class=\"edge\">\n",
+ "<title>3->8</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M725.42,-655.98C633.67,-665.75 334.84,-712.91 229.5,-734.01\"/>\n",
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+ "<g id=\"edge354\" class=\"edge\">\n",
+ "<title>3->7</title>\n",
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+ "<title>3->6</title>\n",
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+ "<g id=\"edge356\" class=\"edge\">\n",
+ "<title>3->5</title>\n",
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+ "<g id=\"edge357\" class=\"edge\">\n",
+ "<title>3->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M725.94,-672.99C711.49,-685.92 694.08,-703.35 681.32,-717.7\"/>\n",
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+ "<g id=\"edge358\" class=\"edge\">\n",
+ "<title>3->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M779.78,-661.56C789.57,-661.7 797.54,-659.45 797.54,-654.81 797.54,-651.99 794.58,-650.05 790.05,-649\"/>\n",
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+ "<title>3->2</title>\n",
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+ "<g id=\"edge360\" class=\"edge\">\n",
+ "<title>3->1</title>\n",
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+ "<title>2->20</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"817.48,-323.1 813.25,-313.39 810.5,-323.62 817.48,-323.1\"/>\n",
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+ "<g id=\"edge362\" class=\"edge\">\n",
+ "<title>2->19</title>\n",
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+ "<g id=\"edge363\" class=\"edge\">\n",
+ "<title>2->18</title>\n",
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"</g>\n",
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"</g>\n",
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+ "<title>1->10</title>\n",
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+ "<title>1->8</title>\n",
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"</g>\n",
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+ "<g id=\"edge394\" class=\"edge\">\n",
+ "<title>1->7</title>\n",
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+ "<g id=\"edge395\" class=\"edge\">\n",
+ "<title>1->6</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M740.4,-201.59C688.53,-291.26 487.93,-684.7 438.82,-792.67\"/>\n",
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"</g>\n",
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+ "<g id=\"edge396\" class=\"edge\">\n",
+ "<title>1->5</title>\n",
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"</g>\n",
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+ "<g id=\"edge397\" class=\"edge\">\n",
+ "<title>1->4</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M746.99,-201.56C728.69,-283.16 675.91,-615.28 665.13,-715.06\"/>\n",
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"</g>\n",
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+ "<g id=\"edge398\" class=\"edge\">\n",
+ "<title>1->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M749.73,-201.52C744.69,-273.57 744.49,-539.22 749.13,-626.69\"/>\n",
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"</g>\n",
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+ "<g id=\"edge399\" class=\"edge\">\n",
+ "<title>1->2</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"797.73,-515.68 803.34,-524.67 804.56,-514.14 797.73,-515.68\"/>\n",
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"</g>\n",
"<!-- 1->1 -->\n",
- "<g id=\"edge800\" class=\"edge\"><title>1->1</title>\n",
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+ "<g id=\"edge400\" class=\"edge\">\n",
+ "<title>1->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M779.78,-190.07C789.57,-190.22 797.54,-187.97 797.54,-183.33 797.54,-180.5 794.58,-178.56 790.05,-177.51\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"812.04\" y=\"-179.63\" font-family=\"Times,serif\" font-size=\"14.00\">K20</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
@@ -5911,7 +6516,7 @@
"<Dot visualization: expr_as_graph [(\"K20\",(1..20)*(1..20))]>"
]
},
- "execution_count": 96,
+ "execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
@@ -5922,7 +6527,7 @@
},
{
"cell_type": "code",
- "execution_count": 97,
+ "execution_count": 77,
"metadata": {},
"outputs": [
{
@@ -5931,7 +6536,7 @@
"Preference changed: DOT_ENGINE = dot\n"
]
},
- "execution_count": 97,
+ "execution_count": 77,
"metadata": {},
"output_type": "execute_result"
}
@@ -5956,7 +6561,7 @@
},
{
"cell_type": "code",
- "execution_count": 98,
+ "execution_count": 78,
"metadata": {},
"outputs": [
{
@@ -5968,7 +6573,7 @@
"{(2↦1),(4↦2),(6↦3),(8↦4),(10↦5)}"
]
},
- "execution_count": 98,
+ "execution_count": 78,
"metadata": {},
"output_type": "execute_result"
}
@@ -5979,7 +6584,7 @@
},
{
"cell_type": "code",
- "execution_count": 99,
+ "execution_count": 79,
"metadata": {},
"outputs": [
{
@@ -5991,7 +6596,7 @@
"{2,4,6,8,10}"
]
},
- "execution_count": 99,
+ "execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
@@ -6002,7 +6607,7 @@
},
{
"cell_type": "code",
- "execution_count": 100,
+ "execution_count": 80,
"metadata": {},
"outputs": [
{
@@ -6014,7 +6619,7 @@
"{1,2,3,4,5}"
]
},
- "execution_count": 100,
+ "execution_count": 80,
"metadata": {},
"output_type": "execute_result"
}
@@ -6025,7 +6630,7 @@
},
{
"cell_type": "code",
- "execution_count": 103,
+ "execution_count": 81,
"metadata": {},
"outputs": [
{
@@ -6037,7 +6642,7 @@
"{2,4,6,8,10}"
]
},
- "execution_count": 103,
+ "execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
@@ -6048,16 +6653,30 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 82,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{(2\\mapsto 1),(4\\mapsto 2),(6\\mapsto 3),(8\\mapsto 4),(10\\mapsto 5)\\}$"
+ ],
+ "text/plain": [
+ "{(2↦1),(4↦2),(6↦3),(8↦4),(10↦5)}"
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":let h {a,b| a∈1..10 ∧ b∈1..10 & b*2=a}"
]
},
{
"cell_type": "code",
- "execution_count": 111,
+ "execution_count": 83,
"metadata": {},
"outputs": [
{
@@ -6066,92 +6685,105 @@
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
" -->\n",
"<!-- Title: state Pages: 1 -->\n",
- "<svg width=\"206pt\" height=\"314pt\"\n",
- " viewBox=\"0.00 0.00 206.00 314.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 310)\">\n",
+ "<svg width=\"206pt\" height=\"305pt\"\n",
+ " viewBox=\"0.00 0.00 206.00 305.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 301)\">\n",
"<title>state</title>\n",
- "<polygon fill=\"white\" stroke=\"white\" points=\"-4,5 -4,-310 203,-310 203,5 -4,5\"/>\n",
+ "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-301 202,-301 202,4 -4,4\"/>\n",
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- "<text text-anchor=\"middle\" x=\"27\" y=\"-283.8\" font-family=\"Times,serif\" font-size=\"14.00\">10</text>\n",
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+ "<title>5</title>\n",
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+ "<text text-anchor=\"middle\" x=\"27\" y=\"-188.3\" font-family=\"Times,serif\" font-size=\"14.00\">5</text>\n",
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- "<g id=\"edge2\" class=\"edge\"><title>10->5</title>\n",
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+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>10->5</title>\n",
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"text/plain": [
- "<Dot visualization: expr_as_graph [dhd={(1,\"nein\"),(2,\"nein\"),(3,\"ja\"),(4,\"nein\"),(5,\"nein\"),(6,\"ja\"),(7,\"nein\")} & h={(2,1),(4,2),(6,3),(8,4),(10,5)}(\"h\",h)]>"
+ "<Dot visualization: expr_as_graph [hh={(2,1),(4,2),(6,3),(8,4),(10,5)}(\"h\",h)]>"
]
},
- "execution_count": 111,
+ "execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
@@ -6162,7 +6794,7 @@
},
{
"cell_type": "code",
- "execution_count": 104,
+ "execution_count": 84,
"metadata": {},
"outputs": [
{
@@ -6174,7 +6806,7 @@
"{(1↦\"nein\"),(2↦\"nein\"),(3↦\"ja\"),(4↦\"nein\"),(5↦\"nein\"),(6↦\"ja\"),(7↦\"nein\")}"
]
},
- "execution_count": 104,
+ "execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
@@ -6185,7 +6817,7 @@
},
{
"cell_type": "code",
- "execution_count": 105,
+ "execution_count": 85,
"metadata": {},
"outputs": [
{
@@ -6197,7 +6829,7 @@
"{1,2,3,4,5,6,7}"
]
},
- "execution_count": 105,
+ "execution_count": 85,
"metadata": {},
"output_type": "execute_result"
}
@@ -6208,7 +6840,7 @@
},
{
"cell_type": "code",
- "execution_count": 106,
+ "execution_count": 86,
"metadata": {},
"outputs": [
{
@@ -6220,7 +6852,7 @@
"{\"ja\",\"nein\"}"
]
},
- "execution_count": 106,
+ "execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
@@ -6231,7 +6863,7 @@
},
{
"cell_type": "code",
- "execution_count": 107,
+ "execution_count": 87,
"metadata": {},
"outputs": [
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@@ -6342,7 +6990,7 @@
"<Dot visualization: expr_as_graph [dhd={(1,\"nein\"),(2,\"nein\"),(3,\"ja\"),(4,\"nein\"),(5,\"nein\"),(6,\"ja\"),(7,\"nein\")} & h={(2,1),(4,2),(6,3),(8,4),(10,5)}(\"d\",d)]>"
]
},
- "execution_count": 107,
+ "execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
@@ -6368,7 +7016,7 @@
},
{
"cell_type": "code",
- "execution_count": 112,
+ "execution_count": 88,
"metadata": {},
"outputs": [
{
@@ -6380,7 +7028,7 @@
"{4,5}"
]
},
- "execution_count": 112,
+ "execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
@@ -6391,7 +7039,7 @@
},
{
"cell_type": "code",
- "execution_count": 110,
+ "execution_count": 89,
"metadata": {},
"outputs": [
{
@@ -6403,7 +7051,7 @@
"{\"ja\"}"
]
},
- "execution_count": 110,
+ "execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
@@ -6414,16 +7062,30 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 90,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\emptyset$"
+ ],
+ "text/plain": [
+ "∅"
+ ]
+ },
+ "execution_count": 90,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"d[{0}]"
]
},
{
"cell_type": "code",
- "execution_count": 113,
+ "execution_count": 91,
"metadata": {},
"outputs": [
{
@@ -6435,7 +7097,7 @@
"{(\"ja\"↦3),(\"ja\"↦6),(\"nein\"↦1),(\"nein\"↦2),(\"nein\"↦4),(\"nein\"↦5),(\"nein\"↦7)}"
]
},
- "execution_count": 113,
+ "execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
@@ -6446,7 +7108,7 @@
},
{
"cell_type": "code",
- "execution_count": 114,
+ "execution_count": 92,
"metadata": {},
"outputs": [
{
@@ -6455,100 +7117,116 @@
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
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- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 130)\">\n",
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- "<polygon fill=\"white\" stroke=\"white\" points=\"-4,5 -4,-130 491,-130 491,5 -4,5\"/>\n",
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+ "<title>"nein"->7</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M140.48,-88.49C129.22,-82.59 116.42,-75.67 105,-69 90.42,-60.48 74.68,-50.54 61.18,-41.77\"/>\n",
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+ "<g id=\"edge2\" class=\"edge\">\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"122.68,-41.54 113.55,-36.18 117.34,-46.07 122.68,-41.54\"/>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"174.5,-46.18 171,-36.18 167.5,-46.18 174.5,-46.18\"/>\n",
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+ "<g id=\"edge4\" class=\"edge\">\n",
+ "<title>"nein"->2</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"224.66,-46.07 228.45,-36.18 219.32,-41.54 224.66,-46.07\"/>\n",
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"</g>\n",
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+ "<g id=\"edge5\" class=\"edge\">\n",
+ "<title>"nein"->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M201.68,-88.74C213.2,-82.82 226.33,-75.82 238,-69 252.56,-60.49 268.24,-50.48 281.63,-41.65\"/>\n",
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"</g>\n",
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+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>"ja"->6</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"401.4,-44.02 394.27,-36.18 394.95,-46.75 401.4,-44.02\"/>\n",
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+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>"ja"->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M430.29,-86.8C435.31,-74.93 442.09,-58.93 447.8,-45.45\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"451.05,-46.75 451.73,-36.18 444.6,-44.02 451.05,-46.75\"/>\n",
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"</g>\n",
"</g>\n",
"</svg>"
@@ -6557,7 +7235,7 @@
"<Dot visualization: expr_as_graph [dhd={(1,\"nein\"),(2,\"nein\"),(3,\"ja\"),(4,\"nein\"),(5,\"nein\"),(6,\"ja\"),(7,\"nein\")} & h={(2,1),(4,2),(6,3),(8,4),(10,5)}(\"d~\",d~)]>"
]
},
- "execution_count": 114,
+ "execution_count": 92,
"metadata": {},
"output_type": "execute_result"
}
@@ -6575,7 +7253,7 @@
},
{
"cell_type": "code",
- "execution_count": 118,
+ "execution_count": 93,
"metadata": {},
"outputs": [
{
@@ -6587,7 +7265,7 @@
"{3,6}"
]
},
- "execution_count": 118,
+ "execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
@@ -6598,7 +7276,7 @@
},
{
"cell_type": "code",
- "execution_count": 119,
+ "execution_count": 94,
"metadata": {},
"outputs": [],
"source": [
@@ -6618,7 +7296,7 @@
},
{
"cell_type": "code",
- "execution_count": 121,
+ "execution_count": 95,
"metadata": {},
"outputs": [
{
@@ -6630,7 +7308,7 @@
"{(1↦4),(1↦8)}"
]
},
- "execution_count": 121,
+ "execution_count": 95,
"metadata": {},
"output_type": "execute_result"
}
@@ -6650,7 +7328,7 @@
},
{
"cell_type": "code",
- "execution_count": 123,
+ "execution_count": 96,
"metadata": {},
"outputs": [
{
@@ -6662,7 +7340,7 @@
"{(4↦1),(8↦2)}"
]
},
- "execution_count": 123,
+ "execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
@@ -6673,7 +7351,7 @@
},
{
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- "execution_count": 124,
+ "execution_count": 97,
"metadata": {},
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@@ -6682,95 +7360,110 @@
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- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 310)\">\n",
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]
},
- "execution_count": 124,
+ "execution_count": 97,
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}
@@ -6790,18 +7483,191 @@
},
{
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- "execution_count": null,
+ "execution_count": 98,
"metadata": {},
- "outputs": [],
+ "outputs": [
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+ "execution_count": 98,
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]
},
{
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+ "execution_count": 99,
"metadata": {},
- "outputs": [],
+ "outputs": [
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+ "execution_count": 99,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":dot expr_as_graph (\"h\",(h))"
]
@@ -6821,7 +7687,7 @@
},
{
"cell_type": "code",
- "execution_count": 125,
+ "execution_count": 100,
"metadata": {},
"outputs": [
{
@@ -6833,7 +7699,7 @@
"{(4↦1),(8↦2)}"
]
},
- "execution_count": 125,
+ "execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
@@ -6844,7 +7710,7 @@
},
{
"cell_type": "code",
- "execution_count": 126,
+ "execution_count": 101,
"metadata": {},
"outputs": [
{
@@ -6856,7 +7722,7 @@
"{(8↦1)}"
]
},
- "execution_count": 126,
+ "execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
@@ -6867,7 +7733,7 @@
},
{
"cell_type": "code",
- "execution_count": 127,
+ "execution_count": 102,
"metadata": {},
"outputs": [
{
@@ -6879,7 +7745,7 @@
"∅"
]
},
- "execution_count": 127,
+ "execution_count": 102,
"metadata": {},
"output_type": "execute_result"
}
@@ -6897,7 +7763,7 @@
},
{
"cell_type": "code",
- "execution_count": 128,
+ "execution_count": 103,
"metadata": {},
"outputs": [
{
@@ -6909,7 +7775,7 @@
"{(2↦1),(4↦1),(4↦2),(6↦3),(8↦1),(8↦2),(8↦4),(10↦5)}"
]
},
- "execution_count": 128,
+ "execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
@@ -6920,7 +7786,7 @@
},
{
"cell_type": "code",
- "execution_count": 129,
+ "execution_count": 104,
"metadata": {},
"outputs": [
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@@ -6929,101 +7795,117 @@
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@@ -7032,7 +7914,7 @@
"<Dot visualization: expr_as_graph [hh={(2,1),(4,2),(6,3),(8,4),(10,5)}(\"h+\",closure1(h))]>"
]
},
- "execution_count": 129,
+ "execution_count": 104,
"metadata": {},
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}
@@ -7043,7 +7925,7 @@
},
{
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- "execution_count": 130,
+ "execution_count": 105,
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"source": [
@@ -7059,7 +7941,7 @@
},
{
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- "execution_count": 131,
+ "execution_count": 106,
"metadata": {},
"outputs": [
{
@@ -7071,7 +7953,7 @@
"{(∅↦{1}),(∅↦{2}),(∅↦{3}),({1}↦{1,2}),({1}↦{1,3}),({1,2}↦{1,2,3}),({1,3}↦{1,2,3}),({2}↦{1,2}),({2}↦{2,3}),({2,3}↦{1,2,3}),({3}↦{1,3}),({3}↦{2,3})}"
]
},
- "execution_count": 131,
+ "execution_count": 106,
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}
@@ -7082,7 +7964,7 @@
},
{
"cell_type": "code",
- "execution_count": 132,
+ "execution_count": 107,
"metadata": {},
"outputs": [
{
@@ -7091,7 +7973,7 @@
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]
},
- "execution_count": 132,
+ "execution_count": 107,
"metadata": {},
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}
@@ -7102,7 +7984,7 @@
},
{
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- "execution_count": 133,
+ "execution_count": 108,
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},
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}
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},
{
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+ "execution_count": 109,
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+ "execution_count": 113,
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"59.92,-133.68 61.31,-123.18 53.67,-130.52 59.92,-133.68\"/>\n",
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"</g>\n",
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+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>1->1</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M54.24,-199.87C64.02,-200.04 72,-197.41 72,-192 72,-188.7 69.04,-186.44 64.51,-185.21\"/>\n",
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@@ -7717,7 +8660,7 @@
"<Dot visualization: expr_as_graph [Arsub1A={1,2,3} & r={(1,2),(2,3)} & sub1={({},{1}),({},{2}),({},{3}),({1},{1,2}),({1},{1,3}),({1,2},{1,2,3}),({1,3},{1,2,3}),({2},{1,2}),({2},{2,3}),({2,3},{1,2,3}),({3},{1,3}),({3},{2,3})}(\"r*\",id(A)\\/r\\/(r;r)\\/((r;r);r)\\/(((r;r);r);r))]>"
]
},
- "execution_count": 141,
+ "execution_count": 116,
"metadata": {},
"output_type": "execute_result"
}
@@ -7735,18 +8678,97 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 117,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{(1\\mapsto 2),(1\\mapsto 3),(2\\mapsto 3)\\}$"
+ ],
+ "text/plain": [
+ "{(1↦2),(1↦3),(2↦3)}"
+ ]
+ },
+ "execution_count": 117,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"closure1(r)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 118,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+ "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+ " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 214)\">\n",
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+ "</g>\n",
+ "<!-- 2->3 -->\n",
+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>2->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M33.48,-86.8C37.9,-75.05 43.85,-59.24 48.89,-45.84\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"52.29,-46.77 52.53,-36.18 45.74,-44.3 52.29,-46.77\"/>\n",
+ "<text text-anchor=\"middle\" x=\"53.5\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\">r+</text>\n",
+ "</g>\n",
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+ "</g>\n",
+ "<!-- 1->2 -->\n",
+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>1->2</title>\n",
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+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"40.26,-131.3 33.47,-123.18 33.71,-133.77 40.26,-131.3\"/>\n",
+ "<text text-anchor=\"middle\" x=\"53.5\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\">r+</text>\n",
+ "</g>\n",
+ "<!-- 1->3 -->\n",
+ "<g id=\"edge2\" class=\"edge\">\n",
+ "<title>1->3</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M63.77,-173.69C65.09,-168.09 66.34,-161.82 67,-156 72.08,-110.95 72.08,-99.05 67,-54 66.71,-51.45 66.31,-48.82 65.84,-46.2\"/>\n",
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+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<Dot visualization: expr_as_graph [Arsub1A={1,2,3} & r={(1,2),(2,3)} & sub1={({},{1}),({},{2}),({},{3}),({1},{1,2}),({1},{1,3}),({1,2},{1,2,3}),({1,3},{1,2,3}),({2},{1,2}),({2},{2,3}),({2,3},{1,2,3}),({3},{1,3}),({3},{2,3})}(\"r+\",closure1(r))]>"
+ ]
+ },
+ "execution_count": 118,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":dot expr_as_graph (\"r+\",closure1(r))"
]
@@ -7760,7 +8782,7 @@
},
{
"cell_type": "code",
- "execution_count": 142,
+ "execution_count": 119,
"metadata": {},
"outputs": [
{
@@ -7772,7 +8794,7 @@
"{1,2}"
]
},
- "execution_count": 142,
+ "execution_count": 119,
"metadata": {},
"output_type": "execute_result"
}
@@ -7790,16 +8812,30 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 120,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$/*@symbolic*/ \\{\\mathit{z\\_},\\mathit{z\\_\\_}\\mid \\mathit{z\\_} \\mapsto \\mathit{z\\_\\_} \\in \\{(1\\mapsto 2),(1\\mapsto 3),(2\\mapsto 3)\\} \\lor \\mathit{z\\_} = \\mathit{z\\_\\_}\\}$"
+ ],
+ "text/plain": [
+ "/*@symbolic*/ {z_,z__∣z_ ↦ z__ ∈ {(1↦2),(1↦3),(2↦3)} ∨ z_ = z__}"
+ ]
+ },
+ "execution_count": 120,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"closure(r)"
]
},
{
"cell_type": "code",
- "execution_count": 143,
+ "execution_count": 121,
"metadata": {},
"outputs": [
{
@@ -7811,7 +8847,7 @@
"{1,2,3}"
]
},
- "execution_count": 143,
+ "execution_count": 121,
"metadata": {},
"output_type": "execute_result"
}
@@ -7822,7 +8858,7 @@
},
{
"cell_type": "code",
- "execution_count": 144,
+ "execution_count": 122,
"metadata": {},
"outputs": [],
"source": [
@@ -7846,7 +8882,7 @@
},
{
"cell_type": "code",
- "execution_count": 145,
+ "execution_count": 123,
"metadata": {},
"outputs": [
{
@@ -7858,7 +8894,7 @@
"{(1↦2),(2↦3),(3↦4),(4↦5),(5↦6),(6↦7),(7↦8),(8↦9),(9↦10),(10↦11)}"
]
},
- "execution_count": 145,
+ "execution_count": 123,
"metadata": {},
"output_type": "execute_result"
}
@@ -7871,12 +8907,12 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Eine Funktion kann also als Mengen von Paaren dargestellt werden. Es sind aber nicht alle Mengen an Paaren auch Funktionen. Zum Beispiel, unsere Relation sub1 von oben ist keine Funktion:"
+ "Eine Funktion kann also als Menge von Paaren dargestellt werden. Es sind aber nicht alle Mengen an Paaren auch Funktionen. Zum Beispiel, unsere Relation sub1 von oben ist keine Funktion:"
]
},
{
"cell_type": "code",
- "execution_count": 146,
+ "execution_count": 124,
"metadata": {},
"outputs": [
{
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- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
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+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>\\{3\\}->\\{2,3\\}</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M58.53,-173.62C58.47,-163.17 60.11,-150.16 67.17,-141 78.24,-126.64 88.33,-130 108.99,-123\"/>\n",
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+ "<g id=\"edge12\" class=\"edge\">\n",
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@@ -8012,7 +9068,7 @@
"<Dot visualization: expr_as_graph [Asub1A={1,2,3} & sub1={({},{1}),({},{2}),({},{3}),({1},{1,2}),({1},{1,3}),({1,2},{1,2,3}),({1,3},{1,2,3}),({2},{1,2}),({2},{2,3}),({2,3},{1,2,3}),({3},{1,3}),({3},{2,3})}(\"sub1\",sub1)]>"
]
},
- "execution_count": 146,
+ "execution_count": 124,
"metadata": {},
"output_type": "execute_result"
}
@@ -8030,9 +9086,23 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 125,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\{(\\emptyset\\mapsto\\{1\\}),(\\emptyset\\mapsto\\{2\\}),(\\emptyset\\mapsto\\{3\\}),(\\{1\\}\\mapsto\\{1,2\\}),(\\{1\\}\\mapsto\\{1,3\\}),(\\{1,2\\}\\mapsto\\{1,2,3\\}),(\\{1,3\\}\\mapsto\\{1,2,3\\}),(\\{2\\}\\mapsto\\{1,2\\}),(\\{2\\}\\mapsto\\{2,3\\}),(\\{2,3\\}\\mapsto\\{1,2,3\\}),(\\{3\\}\\mapsto\\{1,3\\}),(\\{3\\}\\mapsto\\{2,3\\})\\}$"
+ ],
+ "text/plain": [
+ "{(∅↦{1}),(∅↦{2}),(∅↦{3}),({1}↦{1,2}),({1}↦{1,3}),({1,2}↦{1,2,3}),({1,3}↦{1,2,3}),({2}↦{1,2}),({2}↦{2,3}),({2,3}↦{1,2,3}),({3}↦{1,3}),({3}↦{2,3})}"
+ ]
+ },
+ "execution_count": 125,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
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]
@@ -8051,7 +9121,7 @@
},
{
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+ "execution_count": 126,
"metadata": {},
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@@ -8063,7 +9133,7 @@
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},
- "execution_count": 147,
+ "execution_count": 126,
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@@ -8074,7 +9144,7 @@
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+ "execution_count": 127,
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@@ -8086,7 +9156,7 @@
"FALSE"
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},
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@@ -8106,7 +9176,7 @@
},
{
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- "execution_count": 150,
+ "execution_count": 129,
"metadata": {},
"outputs": [
{
@@ -8118,7 +9188,7 @@
"{(1↦2),(2↦3),(3↦4),(4↦5),(5↦6),(6↦7),(7↦8),(8↦9),(9↦10),(10↦11)}"
]
},
- "execution_count": 150,
+ "execution_count": 129,
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@@ -8129,7 +9199,7 @@
},
{
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- "execution_count": 151,
+ "execution_count": 130,
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{
@@ -8149,7 +9219,7 @@
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]
},
- "execution_count": 151,
+ "execution_count": 130,
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@@ -8160,7 +9230,7 @@
},
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+ "execution_count": 131,
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{
@@ -8180,7 +9250,7 @@
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]
},
- "execution_count": 152,
+ "execution_count": 131,
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@@ -8198,7 +9268,7 @@
},
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- "execution_count": 153,
+ "execution_count": 132,
"metadata": {},
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{
@@ -8218,7 +9288,7 @@
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]
},
- "execution_count": 153,
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@@ -8236,7 +9306,7 @@
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+ "execution_count": 133,
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@@ -8248,7 +9318,7 @@
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+ "execution_count": 133,
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@@ -8259,7 +9329,7 @@
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- "execution_count": 155,
+ "execution_count": 134,
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@@ -8271,7 +9341,7 @@
"FALSE"
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+ "execution_count": 134,
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@@ -8282,7 +9352,7 @@
},
{
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- "execution_count": 156,
+ "execution_count": 135,
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{
@@ -8294,7 +9364,7 @@
"{1,2,3,4,5,6,7,8,9,10}"
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},
- "execution_count": 156,
+ "execution_count": 135,
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@@ -8312,7 +9382,7 @@
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+ "execution_count": 136,
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- "execution_count": 158,
+ "execution_count": 137,
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{
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"{1,2,3,4,5,6,7,8,9,10}"
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},
- "execution_count": 158,
+ "execution_count": 137,
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@@ -8368,7 +9438,7 @@
},
{
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- "execution_count": 159,
+ "execution_count": 138,
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{
@@ -8380,7 +9450,7 @@
"{2,3,4,5,6,7,8,9,10,11}"
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},
- "execution_count": 159,
+ "execution_count": 138,
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@@ -8391,7 +9461,7 @@
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+ "execution_count": 139,
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"{5,6}"
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},
- "execution_count": 160,
+ "execution_count": 139,
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@@ -8414,7 +9484,7 @@
},
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"{5}"
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},
- "execution_count": 167,
+ "execution_count": 140,
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@@ -8437,7 +9507,7 @@
},
{
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+ "execution_count": 141,
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"{3}"
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},
- "execution_count": 162,
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@@ -8460,7 +9530,7 @@
},
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+ "execution_count": 142,
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{
@@ -8472,7 +9542,7 @@
"{6}"
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},
- "execution_count": 163,
+ "execution_count": 142,
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}
@@ -8483,7 +9553,7 @@
},
{
"cell_type": "code",
- "execution_count": 164,
+ "execution_count": 143,
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{
@@ -8495,7 +9565,7 @@
"{5,6,7,8,9,10,11}"
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},
- "execution_count": 164,
+ "execution_count": 143,
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@@ -8506,7 +9576,7 @@
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+ "execution_count": 144,
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"{1,2,3}"
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@@ -8536,7 +9606,7 @@
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@@ -8559,7 +9629,7 @@
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@@ -8589,7 +9659,7 @@
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+ "execution_count": 147,
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"outputs": [
{
@@ -8601,7 +9671,7 @@
"∅"
]
},
- "execution_count": 172,
+ "execution_count": 147,
"metadata": {},
"output_type": "execute_result"
}
@@ -8612,7 +9682,7 @@
},
{
"cell_type": "code",
- "execution_count": 173,
+ "execution_count": 148,
"metadata": {},
"outputs": [
{
@@ -8624,7 +9694,7 @@
"{(1↦2),(2↦3),(3↦4),(4↦5),(5↦6),(6↦7),(7↦8),(8↦9),(9↦10),(10↦11)}"
]
},
- "execution_count": 173,
+ "execution_count": 148,
"metadata": {},
"output_type": "execute_result"
}
@@ -8635,17 +9705,17 @@
},
{
"cell_type": "code",
- "execution_count": 174,
+ "execution_count": 149,
"metadata": {},
"outputs": [
{
"ename": "CommandExecutionException",
- "evalue": ":eval: NOT-WELL-DEFINED: \nfunction applied outside of domain (#7): Function argument: 100, function value: {}\n ### Line: 1, Column: 99 until 107\n\n",
+ "evalue": ":eval: NOT-WELL-DEFINED: \nfunction applied outside of domain (#7): Function argument: 100, function value: {}\n ### Line: 2, Column: 0 until 8\n\n",
"output_type": "error",
"traceback": [
"\u001b[1m\u001b[31m:eval: NOT-WELL-DEFINED: \u001b[0m",
"\u001b[1m\u001b[31mfunction applied outside of domain (#7): Function argument: 100, function value: {}\u001b[0m",
- "\u001b[1m\u001b[31m ### Line: 1, Column: 99 until 107\u001b[0m"
+ "\u001b[1m\u001b[31m ### Line: 2, Column: 0 until 8\u001b[0m"
]
}
],
@@ -8662,7 +9732,7 @@
},
{
"cell_type": "code",
- "execution_count": 175,
+ "execution_count": 150,
"metadata": {},
"outputs": [
{
@@ -8674,7 +9744,7 @@
"{{(1↦1),(2↦1)},{(1↦1),(2↦2)},{(1↦2),(2↦1)},{(1↦2),(2↦2)}}"
]
},
- "execution_count": 175,
+ "execution_count": 150,
"metadata": {},
"output_type": "execute_result"
}
@@ -8698,7 +9768,7 @@
},
{
"cell_type": "code",
- "execution_count": 176,
+ "execution_count": 151,
"metadata": {},
"outputs": [
{
@@ -8710,7 +9780,7 @@
"{∅,{(1↦1)},{(1↦1),(2↦1)},{(1↦1),(2↦2)},{(1↦2)},{(1↦2),(2↦1)},{(1↦2),(2↦2)},{(2↦1)},{(2↦2)}}"
]
},
- "execution_count": 176,
+ "execution_count": 151,
"metadata": {},
"output_type": "execute_result"
}
@@ -8721,7 +9791,7 @@
},
{
"cell_type": "code",
- "execution_count": 177,
+ "execution_count": 152,
"metadata": {},
"outputs": [
{
@@ -8741,7 +9811,7 @@
"\ti10 = {(1↦2),(2↦3),(3↦4),(4↦5),(5↦6),(6↦7),(7↦8),(8↦9),(9↦10),(10↦11)}"
]
},
- "execution_count": 177,
+ "execution_count": 152,
"metadata": {},
"output_type": "execute_result"
}
@@ -8759,7 +9829,7 @@
},
{
"cell_type": "code",
- "execution_count": 178,
+ "execution_count": 153,
"metadata": {},
"outputs": [
{
@@ -8771,7 +9841,7 @@
"{∅,{(1↦1)},{(1↦2)},{(2↦1)},{(2↦2)}}"
]
},
- "execution_count": 178,
+ "execution_count": 153,
"metadata": {},
"output_type": "execute_result"
}
@@ -8789,7 +9859,7 @@
},
{
"cell_type": "code",
- "execution_count": 179,
+ "execution_count": 154,
"metadata": {},
"outputs": [
{
@@ -8801,7 +9871,7 @@
"{{(1↦1),(2↦2)},{(1↦2),(2↦1)}}"
]
},
- "execution_count": 179,
+ "execution_count": 154,
"metadata": {},
"output_type": "execute_result"
}
@@ -8819,7 +9889,7 @@
},
{
"cell_type": "code",
- "execution_count": 180,
+ "execution_count": 155,
"metadata": {},
"outputs": [
{
@@ -8831,7 +9901,7 @@
"{{(1↦1),(2↦2)},{(1↦2),(2↦1)}}"
]
},
- "execution_count": 180,
+ "execution_count": 155,
"metadata": {},
"output_type": "execute_result"
}
@@ -8842,7 +9912,7 @@
},
{
"cell_type": "code",
- "execution_count": 181,
+ "execution_count": 156,
"metadata": {},
"outputs": [
{
@@ -8854,7 +9924,7 @@
"{{(1↦1),(2↦2)},{(1↦2),(2↦1)}}"
]
},
- "execution_count": 181,
+ "execution_count": 156,
"metadata": {},
"output_type": "execute_result"
}
@@ -8865,7 +9935,7 @@
},
{
"cell_type": "code",
- "execution_count": 182,
+ "execution_count": 157,
"metadata": {},
"outputs": [],
"source": [
@@ -8916,7 +9986,7 @@
},
{
"cell_type": "code",
- "execution_count": 199,
+ "execution_count": 158,
"metadata": {},
"outputs": [
{
@@ -8928,7 +9998,7 @@
"{(1↦22),(2↦22),(3↦33)}"
]
},
- "execution_count": 199,
+ "execution_count": 158,
"metadata": {},
"output_type": "execute_result"
}
@@ -8939,7 +10009,7 @@
},
{
"cell_type": "code",
- "execution_count": 200,
+ "execution_count": 159,
"metadata": {},
"outputs": [
{
@@ -8951,7 +10021,7 @@
"{(1↦22),(2↦22),(3↦33)}"
]
},
- "execution_count": 200,
+ "execution_count": 159,
"metadata": {},
"output_type": "execute_result"
}
@@ -8962,7 +10032,7 @@
},
{
"cell_type": "code",
- "execution_count": 190,
+ "execution_count": 160,
"metadata": {},
"outputs": [
{
@@ -8971,56 +10041,64 @@
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
" -->\n",
"<!-- Title: state Pages: 1 -->\n",
- "<svg width=\"206pt\" height=\"134pt\"\n",
- " viewBox=\"0.00 0.00 206.00 134.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 130)\">\n",
+ "<svg width=\"206pt\" height=\"131pt\"\n",
+ " viewBox=\"0.00 0.00 206.00 131.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 127)\">\n",
"<title>state</title>\n",
- "<polygon fill=\"white\" stroke=\"white\" points=\"-4,5 -4,-130 203,-130 203,5 -4,5\"/>\n",
+ "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-127 202,-127 202,4 -4,4\"/>\n",
"<!-- 3 -->\n",
- "<g id=\"node1\" class=\"node\"><title>3</title>\n",
- "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"54,-126 0,-126 0,-90 54,-90 54,-126\"/>\n",
- "<text text-anchor=\"middle\" x=\"27\" y=\"-103.8\" font-family=\"Times,serif\" font-size=\"14.00\">3</text>\n",
+ "<g id=\"node1\" class=\"node\">\n",
+ "<title>3</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"54,-123 0,-123 0,-87 54,-87 54,-123\"/>\n",
+ "<text text-anchor=\"middle\" x=\"27\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- 33 -->\n",
- "<g id=\"node3\" class=\"node\"><title>33</title>\n",
- "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"54,-36 0,-36 0,-0 54,-0 54,-36\"/>\n",
- "<text text-anchor=\"middle\" x=\"27\" y=\"-13.8\" font-family=\"Times,serif\" font-size=\"14.00\">33</text>\n",
+ "<g id=\"node2\" class=\"node\">\n",
+ "<title>33</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"54,-36 0,-36 0,0 54,0 54,-36\"/>\n",
+ "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">33</text>\n",
"</g>\n",
"<!-- 3->33 -->\n",
- "<g id=\"edge2\" class=\"edge\"><title>3->33</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M27,-89.614C27,-77.2403 27,-60.3686 27,-46.2198\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"30.5001,-46.0504 27,-36.0504 23.5001,-46.0504 30.5001,-46.0504\"/>\n",
- "<text text-anchor=\"middle\" x=\"32.0533\" y=\"-58.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>3->33</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M27,-86.8C27,-75.16 27,-59.55 27,-46.24\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"30.5,-46.18 27,-36.18 23.5,-46.18 30.5,-46.18\"/>\n",
+ "<text text-anchor=\"middle\" x=\"33\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
"</g>\n",
"<!-- 2 -->\n",
- "<g id=\"node4\" class=\"node\"><title>2</title>\n",
- "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"126,-126 72,-126 72,-90 126,-90 126,-126\"/>\n",
- "<text text-anchor=\"middle\" x=\"99\" y=\"-103.8\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
+ "<g id=\"node3\" class=\"node\">\n",
+ "<title>2</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"126,-123 72,-123 72,-87 126,-87 126,-123\"/>\n",
+ "<text text-anchor=\"middle\" x=\"99\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">2</text>\n",
"</g>\n",
"<!-- 22 -->\n",
- "<g id=\"node6\" class=\"node\"><title>22</title>\n",
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- "<text text-anchor=\"middle\" x=\"135\" y=\"-13.8\" font-family=\"Times,serif\" font-size=\"14.00\">22</text>\n",
+ "<g id=\"node4\" class=\"node\">\n",
+ "<title>22</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"162,-36 108,-36 108,0 162,0 162,-36\"/>\n",
+ "<text text-anchor=\"middle\" x=\"135\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">22</text>\n",
"</g>\n",
"<!-- 2->22 -->\n",
- "<g id=\"edge4\" class=\"edge\"><title>2->22</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M106.112,-89.614C111.274,-76.9977 118.348,-59.7052 124.204,-45.3907\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"127.478,-46.6311 128.025,-36.0504 120.999,-43.9807 127.478,-46.6311\"/>\n",
- "<text text-anchor=\"middle\" x=\"125.053\" y=\"-58.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
+ "<g id=\"edge2\" class=\"edge\">\n",
+ "<title>2->22</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M106.29,-86.8C111.31,-74.93 118.09,-58.93 123.8,-45.45\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"127.05,-46.75 127.73,-36.18 120.6,-44.02 127.05,-46.75\"/>\n",
+ "<text text-anchor=\"middle\" x=\"125\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
"</g>\n",
"<!-- 1 -->\n",
- "<g id=\"node7\" class=\"node\"><title>1</title>\n",
- "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"198,-126 144,-126 144,-90 198,-90 198,-126\"/>\n",
- "<text text-anchor=\"middle\" x=\"171\" y=\"-103.8\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "<g id=\"node5\" class=\"node\">\n",
+ "<title>1</title>\n",
+ "<polygon fill=\"#cdba96\" stroke=\"#cdba96\" points=\"198,-123 144,-123 144,-87 198,-87 198,-123\"/>\n",
+ "<text text-anchor=\"middle\" x=\"171\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
"</g>\n",
"<!-- 1->22 -->\n",
- "<g id=\"edge6\" class=\"edge\"><title>1->22</title>\n",
- "<path fill=\"none\" stroke=\"firebrick\" d=\"M163.888,-89.614C158.726,-76.9977 151.652,-59.7052 145.796,-45.3907\"/>\n",
- "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"149.001,-43.9807 141.975,-36.0504 142.522,-46.6311 149.001,-43.9807\"/>\n",
- "<text text-anchor=\"middle\" x=\"161.053\" y=\"-58.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>1->22</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M163.71,-86.8C158.69,-74.93 151.91,-58.93 146.2,-45.45\"/>\n",
+ "<polygon fill=\"firebrick\" stroke=\"firebrick\" points=\"149.4,-44.02 142.27,-36.18 142.95,-46.75 149.4,-44.02\"/>\n",
+ "<text text-anchor=\"middle\" x=\"161\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\">G</text>\n",
"</g>\n",
"</g>\n",
"</svg>"
@@ -9029,7 +10107,7 @@
"<Dot visualization: expr_as_graph [AGA={1,2,3} & G={(1,22),(2,22),(3,33)}(\"G\",G)]>"
]
},
- "execution_count": 190,
+ "execution_count": 160,
"metadata": {},
"output_type": "execute_result"
}
@@ -9053,7 +10131,7 @@
},
{
"cell_type": "code",
- "execution_count": 191,
+ "execution_count": 161,
"metadata": {},
"outputs": [
{
@@ -9065,7 +10143,7 @@
"22"
]
},
- "execution_count": 191,
+ "execution_count": 161,
"metadata": {},
"output_type": "execute_result"
}
@@ -9083,7 +10161,7 @@
},
{
"cell_type": "code",
- "execution_count": 192,
+ "execution_count": 162,
"metadata": {},
"outputs": [
{
@@ -9095,7 +10173,7 @@
"3"
]
},
- "execution_count": 192,
+ "execution_count": 162,
"metadata": {},
"output_type": "execute_result"
}
@@ -9106,7 +10184,7 @@
},
{
"cell_type": "code",
- "execution_count": 193,
+ "execution_count": 163,
"metadata": {},
"outputs": [
{
@@ -9118,7 +10196,7 @@
"3"
]
},
- "execution_count": 193,
+ "execution_count": 163,
"metadata": {},
"output_type": "execute_result"
}
@@ -9136,7 +10214,7 @@
},
{
"cell_type": "code",
- "execution_count": 194,
+ "execution_count": 164,
"metadata": {},
"outputs": [
{
@@ -9148,7 +10226,7 @@
"{1,2,3}"
]
},
- "execution_count": 194,
+ "execution_count": 164,
"metadata": {},
"output_type": "execute_result"
}
@@ -9159,7 +10237,7 @@
},
{
"cell_type": "code",
- "execution_count": 195,
+ "execution_count": 165,
"metadata": {},
"outputs": [
{
@@ -9171,7 +10249,7 @@
"{22,33}"
]
},
- "execution_count": 195,
+ "execution_count": 165,
"metadata": {},
"output_type": "execute_result"
}
@@ -9182,7 +10260,7 @@
},
{
"cell_type": "code",
- "execution_count": 196,
+ "execution_count": 166,
"metadata": {},
"outputs": [
{
@@ -9194,7 +10272,7 @@
"{1,2}"
]
},
- "execution_count": 196,
+ "execution_count": 166,
"metadata": {},
"output_type": "execute_result"
}
@@ -9205,7 +10283,7 @@
},
{
"cell_type": "code",
- "execution_count": 197,
+ "execution_count": 167,
"metadata": {},
"outputs": [],
"source": [
diff --git a/info4/kapitel-1/Grammatiken.ipynb b/info4/kapitel-1/Grammatiken.ipynb
index be926db3ae5ee0fbaa407572335c0b884a098387..b7f35c32954122df213dfe0f30879693743d4be0 100644
--- a/info4/kapitel-1/Grammatiken.ipynb
+++ b/info4/kapitel-1/Grammatiken.ipynb
@@ -6,7 +6,7 @@
"source": [
"## Grammatiken und Chomsky-Hierarchie\n",
"\n",
- "Dieses Notebook begleitet Teil 2 der Vorlesung 3 und führt am Ende die Chomsky-Hierarchie ein"
+ "Dieses Notebook begleitet Teil 2 der Vorlesung 3 und führt am Ende die Chomsky-Hierarchie ein."
]
},
{
@@ -625,7 +625,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Wenn wir mit $\\Sigma^*$ schneiden bekommen wir Wörter der von der Grammatik generierten Sprache:"
+ "Wenn wir mit $\\Sigma^*$ schneiden, bekommen wir Wörter der von der Grammatik generierten Sprache:"
]
},
{
@@ -1804,7 +1804,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Die obige Tabelle zeigt, in welche Sprachklasse die entsprechenden Grammatiken fallen. Dabei ist zu beachten, dass L3 = L4 ist, aber P3 und P4 unterschiedliche Typen haben. Die Sprache fällt allerdings immer in die größte Spracheklasse zu der es eine Grammatik gibt, die diese Sprache erzeugt. Also gilt $L4 ∈ \\mathfrak{L}_3 = REG$. Daher reicht die Angabe einer Grammatik nicht aus, um zu zeigen dass eine Sprache höchstens in einer der Klassen liegt. Um dies zu zeigen gibt es verschiedene Methoden, wie z.B. das Pumping-Lemma oder die Myhill-Nerode Relation."
+ "Die obige Tabelle zeigt, in welche Sprachklasse die entsprechenden Grammatiken fallen. Dabei ist zu beachten, dass L3 = L4 ist, aber P3 und P4 unterschiedliche Typen haben. Die Sprache fällt allerdings immer in die größte Spracheklasse zu der es eine Grammatik gibt, die diese Sprache erzeugt. Also gilt $L4 ∈ \\mathfrak{L}_3 = REG$. Daher reicht die Angabe einer Grammatik nicht aus, um zu zeigen, dass eine Sprache höchstens in einer der Klassen liegt. Um dies zu zeigen, gibt es verschiedene Methoden, wie z.B. das Pumping-Lemma oder die Myhill-Nerode Relation."
]
},
{
diff --git a/info4/kapitel-11/PCP.ipynb b/info4/kapitel-11/PCP.ipynb
index 848d689913ad559f027581b011ece86eab95d4dd..35951dcc3b2658fa60fac8511a76d56dc30b9a58 100644
--- a/info4/kapitel-11/PCP.ipynb
+++ b/info4/kapitel-11/PCP.ipynb
@@ -33,7 +33,7 @@
},
{
"cell_type": "code",
- "execution_count": 190,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -42,7 +42,7 @@
"Loaded machine: PostCorrespondence_MC"
]
},
- "execution_count": 190,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -85,7 +85,7 @@
},
{
"cell_type": "code",
- "execution_count": 191,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -94,7 +94,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 191,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -105,7 +105,7 @@
},
{
"cell_type": "code",
- "execution_count": 192,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -114,7 +114,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 192,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -125,7 +125,7 @@
},
{
"cell_type": "code",
- "execution_count": 193,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -137,7 +137,7 @@
"[([1]↦[1,0]),([0,1]↦[1]),([0,1,0]↦[1,0,0])]"
]
},
- "execution_count": 193,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -148,7 +148,7 @@
},
{
"cell_type": "code",
- "execution_count": 194,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -167,7 +167,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 194,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -178,7 +178,7 @@
},
{
"cell_type": "code",
- "execution_count": 195,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -192,7 +192,7 @@
"Schritt(1,[1],[1,0])"
]
},
- "execution_count": 195,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -210,7 +210,7 @@
},
{
"cell_type": "code",
- "execution_count": 196,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -219,7 +219,7 @@
"Executed operation: Schritt(1,[1],[1,0])"
]
},
- "execution_count": 196,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -230,7 +230,7 @@
},
{
"cell_type": "code",
- "execution_count": 197,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -253,7 +253,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 197,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -264,7 +264,7 @@
},
{
"cell_type": "code",
- "execution_count": 198,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -276,7 +276,7 @@
"[1]"
]
},
- "execution_count": 198,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -287,7 +287,7 @@
},
{
"cell_type": "code",
- "execution_count": 199,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -299,7 +299,7 @@
"[1,0]"
]
},
- "execution_count": 199,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -310,7 +310,7 @@
},
{
"cell_type": "code",
- "execution_count": 200,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -325,7 +325,7 @@
"Schritt(3,[0,1,0],[1,0,0])"
]
},
- "execution_count": 200,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -343,7 +343,7 @@
},
{
"cell_type": "code",
- "execution_count": 201,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -352,7 +352,7 @@
"Executed operation: Schritt(2,[0,1],[1])"
]
},
- "execution_count": 201,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -363,7 +363,7 @@
},
{
"cell_type": "code",
- "execution_count": 202,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -388,7 +388,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 202,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -399,7 +399,7 @@
},
{
"cell_type": "code",
- "execution_count": 203,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -408,7 +408,7 @@
"Executed operation: Lösung()"
]
},
- "execution_count": 203,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -427,7 +427,7 @@
},
{
"cell_type": "code",
- "execution_count": 204,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -449,7 +449,7 @@
"4: Lösung() (current)"
]
},
- "execution_count": 204,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -460,7 +460,7 @@
},
{
"cell_type": "code",
- "execution_count": 205,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -469,7 +469,7 @@
"Changed to state with index 2"
]
},
- "execution_count": 205,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -480,7 +480,7 @@
},
{
"cell_type": "code",
- "execution_count": 206,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -503,7 +503,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 206,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -514,7 +514,7 @@
},
{
"cell_type": "code",
- "execution_count": 207,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -523,7 +523,7 @@
"Executed operation: Schritt(3,[0,1,0],[1,0,0])"
]
},
- "execution_count": 207,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -534,7 +534,7 @@
},
{
"cell_type": "code",
- "execution_count": 208,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -563,7 +563,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 208,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -574,7 +574,7 @@
},
{
"cell_type": "code",
- "execution_count": 209,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -583,7 +583,7 @@
"Executed operation: Schritt(3,[0,1,0],[1,0,0])"
]
},
- "execution_count": 209,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -594,7 +594,7 @@
},
{
"cell_type": "code",
- "execution_count": 210,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
@@ -629,7 +629,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 210,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -640,7 +640,7 @@
},
{
"cell_type": "code",
- "execution_count": 211,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
@@ -649,7 +649,7 @@
"Executed operation: Schritt(2,[0,1],[1])"
]
},
- "execution_count": 211,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -660,7 +660,7 @@
},
{
"cell_type": "code",
- "execution_count": 212,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -697,7 +697,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 212,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -708,7 +708,7 @@
},
{
"cell_type": "code",
- "execution_count": 213,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
@@ -717,7 +717,7 @@
"Executed operation: Lösung()"
]
},
- "execution_count": 213,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -728,7 +728,7 @@
},
{
"cell_type": "code",
- "execution_count": 214,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -754,7 +754,7 @@
"6: Lösung() (current)"
]
},
- "execution_count": 214,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -770,7 +770,7 @@
"Sie können das B Modell oben mit anderen Werten für K ausprobieren:\n",
"- K = [ [0,1]↦[1], [0,1,0]↦[1,0,0], [1]↦[1,0] ] Problem von Folie 36 */\n",
"- K = [ [1]↦[1,0,1], [1,0]↦[0,0], [0,1,1]↦[1,1] ] \n",
- "- K = [ [0,0,1]↦[0], [0,1]↦[0,1,1], [0,1]↦[1,0,1], [1,0] ↦ [0,0,1] ], Problem von Folie 32; kleinse Lösung hat 66 Elemente\n",
+ "- K = [ [0,0,1]↦[0], [0,1]↦[0,1,1], [0,1]↦[1,0,1], [1,0] ↦ [0,0,1] ], Problem von Folie 32; kleinste Lösung hat 66 Elemente\n",
"\n",
"Hier erst einmal Illustration der Lösung von Folie 36.\n",
"Folgende Maschine hat keinen vordefinierten Wert von K; man muss diesen der :constants Anweisung übergeben."
@@ -778,7 +778,7 @@
},
{
"cell_type": "code",
- "execution_count": 215,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -787,7 +787,7 @@
"Loaded machine: PostCorrespondence_MC"
]
},
- "execution_count": 215,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -830,7 +830,7 @@
},
{
"cell_type": "code",
- "execution_count": 216,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -839,7 +839,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 216,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -850,7 +850,7 @@
},
{
"cell_type": "code",
- "execution_count": 217,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -859,7 +859,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 217,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -870,7 +870,7 @@
},
{
"cell_type": "code",
- "execution_count": 218,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -879,7 +879,7 @@
"Executed operation: Schritt(3,[1],[1,0])"
]
},
- "execution_count": 218,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -890,7 +890,7 @@
},
{
"cell_type": "code",
- "execution_count": 219,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -913,7 +913,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 219,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -924,7 +924,7 @@
},
{
"cell_type": "code",
- "execution_count": 220,
+ "execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -933,7 +933,7 @@
"Executed operation: Schritt(2,[0,1,0],[1,0,0])"
]
},
- "execution_count": 220,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -944,7 +944,7 @@
},
{
"cell_type": "code",
- "execution_count": 221,
+ "execution_count": 32,
"metadata": {},
"outputs": [
{
@@ -973,7 +973,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 221,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -984,7 +984,7 @@
},
{
"cell_type": "code",
- "execution_count": 222,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -993,7 +993,7 @@
"Executed operation: Schritt(2,[0,1,0],[1,0,0])"
]
},
- "execution_count": 222,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@@ -1004,7 +1004,7 @@
},
{
"cell_type": "code",
- "execution_count": 223,
+ "execution_count": 34,
"metadata": {},
"outputs": [
{
@@ -1039,7 +1039,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 223,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -1050,7 +1050,7 @@
},
{
"cell_type": "code",
- "execution_count": 224,
+ "execution_count": 35,
"metadata": {},
"outputs": [
{
@@ -1059,7 +1059,7 @@
"Executed operation: Schritt(1,[0,1],[1])"
]
},
- "execution_count": 224,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -1070,7 +1070,7 @@
},
{
"cell_type": "code",
- "execution_count": 225,
+ "execution_count": 36,
"metadata": {},
"outputs": [
{
@@ -1107,7 +1107,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 225,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -1125,7 +1125,7 @@
},
{
"cell_type": "code",
- "execution_count": 226,
+ "execution_count": 37,
"metadata": {},
"outputs": [
{
@@ -1134,7 +1134,7 @@
"Changed to state with index -1"
]
},
- "execution_count": 226,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -1145,7 +1145,7 @@
},
{
"cell_type": "code",
- "execution_count": 227,
+ "execution_count": 38,
"metadata": {},
"outputs": [
{
@@ -1154,7 +1154,7 @@
"Machine constants set up using operation 11: $setup_constants()"
]
},
- "execution_count": 227,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
@@ -1165,7 +1165,7 @@
},
{
"cell_type": "code",
- "execution_count": 228,
+ "execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1174,7 +1174,7 @@
"Machine initialised using operation 12: $initialise_machine()"
]
},
- "execution_count": 228,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -1185,7 +1185,7 @@
},
{
"cell_type": "code",
- "execution_count": 229,
+ "execution_count": 40,
"metadata": {},
"outputs": [
{
@@ -1200,7 +1200,7 @@
"Schritt(2,[0,1],[0,1,1])"
]
},
- "execution_count": 229,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -1211,7 +1211,7 @@
},
{
"cell_type": "code",
- "execution_count": 230,
+ "execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -1220,7 +1220,7 @@
"Executed operation: Schritt(2,[0,1],[0,1,1])"
]
},
- "execution_count": 230,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
@@ -1231,7 +1231,7 @@
},
{
"cell_type": "code",
- "execution_count": 231,
+ "execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -1240,7 +1240,7 @@
"Executed operation: Schritt(4,[1,0],[0,0,1])"
]
},
- "execution_count": 231,
+ "execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
@@ -1251,7 +1251,7 @@
},
{
"cell_type": "code",
- "execution_count": 232,
+ "execution_count": 43,
"metadata": {},
"outputs": [
{
@@ -1282,7 +1282,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 232,
+ "execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
@@ -1300,7 +1300,7 @@
},
{
"cell_type": "code",
- "execution_count": 233,
+ "execution_count": 44,
"metadata": {},
"outputs": [
{
@@ -1309,7 +1309,7 @@
"Executed operation: Schritt(3,[0,1],[1,0,1])"
]
},
- "execution_count": 233,
+ "execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
@@ -1320,7 +1320,7 @@
},
{
"cell_type": "code",
- "execution_count": 234,
+ "execution_count": 45,
"metadata": {},
"outputs": [
{
@@ -1329,7 +1329,7 @@
"Executed operation: Schritt(4,[1,0],[0,0,1])"
]
},
- "execution_count": 234,
+ "execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
@@ -1340,7 +1340,7 @@
},
{
"cell_type": "code",
- "execution_count": 235,
+ "execution_count": 46,
"metadata": {},
"outputs": [
{
@@ -1349,7 +1349,7 @@
"Executed operation: Schritt(4,[1,0],[0,0,1])"
]
},
- "execution_count": 235,
+ "execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
@@ -1360,7 +1360,7 @@
},
{
"cell_type": "code",
- "execution_count": 236,
+ "execution_count": 47,
"metadata": {},
"outputs": [
{
@@ -1369,7 +1369,7 @@
"Executed operation: Schritt(2,[0,1],[0,1,1])"
]
},
- "execution_count": 236,
+ "execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
@@ -1380,7 +1380,7 @@
},
{
"cell_type": "code",
- "execution_count": 237,
+ "execution_count": 48,
"metadata": {},
"outputs": [
{
@@ -1435,7 +1435,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 237,
+ "execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
@@ -1526,15 +1526,15 @@
"## Kodierung des Halteproblems als MPCP Problem\n",
"\n",
"Folgende B Maschine kodiert das Halteproblem einer Turingmaschine als MPCP Problem.\n",
- "Der erste Schritt zu einer Lösung wird in der Initialisierung kodiert; dort wir erzwungen, dass wir das erste Paar aus dem Skript $(\\#,\\# z_0 w)$ benutzen.\n",
+ "Der erste Schritt zu einer Lösung wird in der Initialisierung kodiert; dort wird erzwungen, dass wir das erste Paar aus dem Skript $(\\#,\\# z_0 w \\#)$ benutzen.\n",
"Die Turing Maschine hat 3 Zustände: z0,z1,z2.\n",
"z2 ist der Endzustand.\n",
- "z0 akzeptiert a and wechselt bei einem b zu z1, z1 akzeptiert b's und geht zu z2 bei einem Blank. \n"
+ "z0 akzeptiert a and wechselt bei einem b zu z1, z1 akzeptiert b's und geht zu z2 bei einem Blank. "
]
},
{
"cell_type": "code",
- "execution_count": 238,
+ "execution_count": 49,
"metadata": {},
"outputs": [
{
@@ -1543,7 +1543,7 @@
"Loaded machine: PostCorrespondence_Turing_MC"
]
},
- "execution_count": 238,
+ "execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
@@ -1593,7 +1593,7 @@
},
{
"cell_type": "code",
- "execution_count": 239,
+ "execution_count": 50,
"metadata": {},
"outputs": [
{
@@ -1602,7 +1602,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 239,
+ "execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
@@ -1613,7 +1613,7 @@
},
{
"cell_type": "code",
- "execution_count": 240,
+ "execution_count": 51,
"metadata": {},
"outputs": [
{
@@ -1622,7 +1622,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 240,
+ "execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
@@ -1633,7 +1633,7 @@
},
{
"cell_type": "code",
- "execution_count": 241,
+ "execution_count": 52,
"metadata": {},
"outputs": [
{
@@ -1662,7 +1662,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 241,
+ "execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
@@ -1673,7 +1673,7 @@
},
{
"cell_type": "code",
- "execution_count": 242,
+ "execution_count": 53,
"metadata": {},
"outputs": [
{
@@ -1687,7 +1687,7 @@
"Schritt(4,[z0,a],[a,z0])"
]
},
- "execution_count": 242,
+ "execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
@@ -1698,7 +1698,7 @@
},
{
"cell_type": "code",
- "execution_count": 243,
+ "execution_count": 54,
"metadata": {},
"outputs": [
{
@@ -1707,7 +1707,7 @@
"Executed operation: Schritt(4,[z0,a],[a,z0])"
]
},
- "execution_count": 243,
+ "execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
@@ -1718,7 +1718,7 @@
},
{
"cell_type": "code",
- "execution_count": 244,
+ "execution_count": 55,
"metadata": {},
"outputs": [
{
@@ -1751,7 +1751,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 244,
+ "execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
@@ -1770,7 +1770,7 @@
},
{
"cell_type": "code",
- "execution_count": 245,
+ "execution_count": 56,
"metadata": {},
"outputs": [
{
@@ -1784,7 +1784,7 @@
"Schritt(2,[b],[b])"
]
},
- "execution_count": 245,
+ "execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
@@ -1795,7 +1795,7 @@
},
{
"cell_type": "code",
- "execution_count": 246,
+ "execution_count": 57,
"metadata": {},
"outputs": [
{
@@ -1804,7 +1804,7 @@
"Executed operation: Schritt(2,[b],[b])"
]
},
- "execution_count": 246,
+ "execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
@@ -1815,7 +1815,7 @@
},
{
"cell_type": "code",
- "execution_count": 247,
+ "execution_count": 58,
"metadata": {},
"outputs": [
{
@@ -1829,7 +1829,7 @@
"Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 247,
+ "execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
@@ -1840,7 +1840,7 @@
},
{
"cell_type": "code",
- "execution_count": 248,
+ "execution_count": 59,
"metadata": {},
"outputs": [
{
@@ -1849,7 +1849,7 @@
"Executed operation: Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 248,
+ "execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
@@ -1860,7 +1860,7 @@
},
{
"cell_type": "code",
- "execution_count": 249,
+ "execution_count": 60,
"metadata": {},
"outputs": [
{
@@ -1897,7 +1897,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 249,
+ "execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
@@ -1908,7 +1908,7 @@
},
{
"cell_type": "code",
- "execution_count": 250,
+ "execution_count": 61,
"metadata": {},
"outputs": [
{
@@ -1922,7 +1922,7 @@
"Schritt(1,[a],[a])"
]
},
- "execution_count": 250,
+ "execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
@@ -1940,7 +1940,7 @@
},
{
"cell_type": "code",
- "execution_count": 251,
+ "execution_count": 62,
"metadata": {},
"outputs": [
{
@@ -1949,7 +1949,7 @@
"Executed operation: Schritt(1,[a],[a])"
]
},
- "execution_count": 251,
+ "execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
@@ -1960,7 +1960,7 @@
},
{
"cell_type": "code",
- "execution_count": 252,
+ "execution_count": 63,
"metadata": {},
"outputs": [
{
@@ -1999,7 +1999,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 252,
+ "execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
@@ -2010,7 +2010,7 @@
},
{
"cell_type": "code",
- "execution_count": 253,
+ "execution_count": 64,
"metadata": {},
"outputs": [
{
@@ -2024,7 +2024,7 @@
"Schritt(5,[z0,b],[b,z1])"
]
},
- "execution_count": 253,
+ "execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
@@ -2035,7 +2035,7 @@
},
{
"cell_type": "code",
- "execution_count": 254,
+ "execution_count": 65,
"metadata": {},
"outputs": [
{
@@ -2044,7 +2044,7 @@
"Executed operation: Schritt(5,[z0,b],[b,z1])"
]
},
- "execution_count": 254,
+ "execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
@@ -2055,7 +2055,7 @@
},
{
"cell_type": "code",
- "execution_count": 255,
+ "execution_count": 66,
"metadata": {},
"outputs": [
{
@@ -2098,7 +2098,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 255,
+ "execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
@@ -2116,7 +2116,7 @@
},
{
"cell_type": "code",
- "execution_count": 256,
+ "execution_count": 67,
"metadata": {},
"outputs": [
{
@@ -2125,7 +2125,7 @@
"Executed operation: Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 256,
+ "execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
@@ -2136,7 +2136,7 @@
},
{
"cell_type": "code",
- "execution_count": 257,
+ "execution_count": 68,
"metadata": {},
"outputs": [
{
@@ -2145,7 +2145,7 @@
"Executed operation: Schritt(1,[a],[a])"
]
},
- "execution_count": 257,
+ "execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
@@ -2156,7 +2156,7 @@
},
{
"cell_type": "code",
- "execution_count": 258,
+ "execution_count": 69,
"metadata": {},
"outputs": [
{
@@ -2203,7 +2203,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 258,
+ "execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
@@ -2214,7 +2214,7 @@
},
{
"cell_type": "code",
- "execution_count": 259,
+ "execution_count": 70,
"metadata": {},
"outputs": [
{
@@ -2223,7 +2223,7 @@
"Executed operation: Schritt(2,[b],[b])"
]
},
- "execution_count": 259,
+ "execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
@@ -2234,7 +2234,7 @@
},
{
"cell_type": "code",
- "execution_count": 260,
+ "execution_count": 71,
"metadata": {},
"outputs": [
{
@@ -2283,7 +2283,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 260,
+ "execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
@@ -2294,7 +2294,7 @@
},
{
"cell_type": "code",
- "execution_count": 261,
+ "execution_count": 72,
"metadata": {},
"outputs": [
{
@@ -2308,7 +2308,7 @@
"Schritt(7,[z1,Hash],[z2,Hash])"
]
},
- "execution_count": 261,
+ "execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
@@ -2319,7 +2319,7 @@
},
{
"cell_type": "code",
- "execution_count": 262,
+ "execution_count": 73,
"metadata": {},
"outputs": [
{
@@ -2328,7 +2328,7 @@
"Executed operation: Schritt(7,[z1,Hash],[z2,Hash])"
]
},
- "execution_count": 262,
+ "execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
@@ -2339,7 +2339,7 @@
},
{
"cell_type": "code",
- "execution_count": 263,
+ "execution_count": 74,
"metadata": {},
"outputs": [
{
@@ -2392,7 +2392,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 263,
+ "execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
@@ -2410,7 +2410,7 @@
},
{
"cell_type": "code",
- "execution_count": 264,
+ "execution_count": 75,
"metadata": {},
"outputs": [
{
@@ -2424,7 +2424,7 @@
"Schritt(1,[a],[a])"
]
},
- "execution_count": 264,
+ "execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
@@ -2435,7 +2435,7 @@
},
{
"cell_type": "code",
- "execution_count": 265,
+ "execution_count": 76,
"metadata": {},
"outputs": [
{
@@ -2444,7 +2444,7 @@
"Executed operation: Schritt(1,[a],[a])"
]
},
- "execution_count": 265,
+ "execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
@@ -2455,7 +2455,7 @@
},
{
"cell_type": "code",
- "execution_count": 266,
+ "execution_count": 77,
"metadata": {},
"outputs": [
{
@@ -2510,7 +2510,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 266,
+ "execution_count": 77,
"metadata": {},
"output_type": "execute_result"
}
@@ -2521,7 +2521,7 @@
},
{
"cell_type": "code",
- "execution_count": 267,
+ "execution_count": 78,
"metadata": {},
"outputs": [
{
@@ -2536,7 +2536,7 @@
"Schritt(9,[b,z2],[z2])"
]
},
- "execution_count": 267,
+ "execution_count": 78,
"metadata": {},
"output_type": "execute_result"
}
@@ -2554,7 +2554,7 @@
},
{
"cell_type": "code",
- "execution_count": 268,
+ "execution_count": 79,
"metadata": {},
"outputs": [
{
@@ -2563,7 +2563,7 @@
"Executed operation: Schritt(9,[b,z2],[z2])"
]
},
- "execution_count": 268,
+ "execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
@@ -2574,7 +2574,7 @@
},
{
"cell_type": "code",
- "execution_count": 269,
+ "execution_count": 80,
"metadata": {},
"outputs": [
{
@@ -2631,7 +2631,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 269,
+ "execution_count": 80,
"metadata": {},
"output_type": "execute_result"
}
@@ -2642,7 +2642,7 @@
},
{
"cell_type": "code",
- "execution_count": 270,
+ "execution_count": 81,
"metadata": {},
"outputs": [
{
@@ -2656,7 +2656,7 @@
"Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 270,
+ "execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
@@ -2667,7 +2667,7 @@
},
{
"cell_type": "code",
- "execution_count": 271,
+ "execution_count": 82,
"metadata": {},
"outputs": [
{
@@ -2676,7 +2676,7 @@
"Executed operation: Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 271,
+ "execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
@@ -2687,7 +2687,7 @@
},
{
"cell_type": "code",
- "execution_count": 272,
+ "execution_count": 83,
"metadata": {},
"outputs": [
{
@@ -2746,7 +2746,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 272,
+ "execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
@@ -2757,7 +2757,7 @@
},
{
"cell_type": "code",
- "execution_count": 273,
+ "execution_count": 84,
"metadata": {},
"outputs": [
{
@@ -2772,7 +2772,7 @@
"Schritt(8,[a,z2],[z2])"
]
},
- "execution_count": 273,
+ "execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
@@ -2790,7 +2790,7 @@
},
{
"cell_type": "code",
- "execution_count": 274,
+ "execution_count": 85,
"metadata": {},
"outputs": [
{
@@ -2799,7 +2799,7 @@
"Executed operation: Schritt(8,[a,z2],[z2])"
]
},
- "execution_count": 274,
+ "execution_count": 85,
"metadata": {},
"output_type": "execute_result"
}
@@ -2810,7 +2810,7 @@
},
{
"cell_type": "code",
- "execution_count": 275,
+ "execution_count": 86,
"metadata": {},
"outputs": [
{
@@ -2871,7 +2871,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 275,
+ "execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
@@ -2882,7 +2882,7 @@
},
{
"cell_type": "code",
- "execution_count": 276,
+ "execution_count": 87,
"metadata": {},
"outputs": [
{
@@ -2891,7 +2891,7 @@
"Executed operation: Schritt(3,[Hash],[Hash])"
]
},
- "execution_count": 276,
+ "execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
@@ -2902,7 +2902,7 @@
},
{
"cell_type": "code",
- "execution_count": 277,
+ "execution_count": 88,
"metadata": {},
"outputs": [
{
@@ -2965,7 +2965,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 277,
+ "execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
@@ -2976,7 +2976,7 @@
},
{
"cell_type": "code",
- "execution_count": 278,
+ "execution_count": 89,
"metadata": {},
"outputs": [
{
@@ -2990,7 +2990,7 @@
"Schritt(10,[z2,Hash,Hash],[Hash])"
]
},
- "execution_count": 278,
+ "execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
@@ -3008,7 +3008,7 @@
},
{
"cell_type": "code",
- "execution_count": 279,
+ "execution_count": 90,
"metadata": {},
"outputs": [
{
@@ -3017,7 +3017,7 @@
"Executed operation: Schritt(10,[z2,Hash,Hash],[Hash])"
]
},
- "execution_count": 279,
+ "execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
@@ -3028,7 +3028,7 @@
},
{
"cell_type": "code",
- "execution_count": 280,
+ "execution_count": 91,
"metadata": {},
"outputs": [
{
@@ -3093,7 +3093,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 280,
+ "execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
@@ -3104,7 +3104,7 @@
},
{
"cell_type": "code",
- "execution_count": 281,
+ "execution_count": 92,
"metadata": {},
"outputs": [
{
@@ -3113,7 +3113,7 @@
"Executed operation: Lösung()"
]
},
- "execution_count": 281,
+ "execution_count": 92,
"metadata": {},
"output_type": "execute_result"
}
diff --git a/info4/kapitel-2/DFA.ipynb b/info4/kapitel-2/DFA.ipynb
index dc0fca0ed30292f548b7644c6c939b34ce199ce5..1182c2660b38bacda49b1cae10aa21f42526a555 100644
--- a/info4/kapitel-2/DFA.ipynb
+++ b/info4/kapitel-2/DFA.ipynb
@@ -37,7 +37,7 @@
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -46,7 +46,7 @@
"Loaded machine: DFA"
]
},
- "execution_count": 2,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -80,7 +80,7 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -89,7 +89,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 3,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -109,7 +109,7 @@
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -121,7 +121,7 @@
"z1"
]
},
- "execution_count": 4,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -139,7 +139,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -151,7 +151,7 @@
"z2"
]
},
- "execution_count": 5,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -194,7 +194,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -206,7 +206,7 @@
"FALSE"
]
},
- "execution_count": 6,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -242,7 +242,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -251,90 +251,104 @@
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
" -->\n",
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- "<svg width=\"540pt\" height=\"717pt\"\n",
- " viewBox=\"0.00 0.00 540.00 717.37\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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+ "<svg width=\"540pt\" height=\"716pt\"\n",
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+ "<title>1->2</title>\n",
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+ "<title>3</title>\n",
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]
},
- "execution_count": 7,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -365,7 +379,7 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
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]
},
- "execution_count": 8,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
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},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
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]
},
- "execution_count": 9,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -460,7 +474,7 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -469,7 +483,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 10,
+ "execution_count": 9,
"metadata": {},
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}
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},
{
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+ "execution_count": 10,
"metadata": {},
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]
},
- "execution_count": 17,
+ "execution_count": 10,
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{
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+ "execution_count": 11,
"metadata": {},
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{
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]
},
- "execution_count": 19,
+ "execution_count": 11,
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},
{
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+ "execution_count": 12,
"metadata": {},
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]
},
- "execution_count": 20,
+ "execution_count": 12,
"metadata": {},
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{
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+ "execution_count": 13,
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{
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]
},
- "execution_count": 21,
+ "execution_count": 13,
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{
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- "execution_count": 22,
+ "execution_count": 14,
"metadata": {},
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{
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]
},
- "execution_count": 22,
+ "execution_count": 14,
"metadata": {},
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{
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- "execution_count": 23,
+ "execution_count": 15,
"metadata": {},
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]
},
- "execution_count": 23,
+ "execution_count": 15,
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- "\\item für $x = a_1 a_2 \\cdots a_n$ in $\\Sigma^*$ gilt:\n",
+ "\n",
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},
{
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- "execution_count": 24,
+ "execution_count": 16,
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},
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"<Dot visualization: custom_graph []>"
]
},
- "execution_count": 7,
+ "execution_count": 27,
"metadata": {},
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}
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":dot custom_graph"
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- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
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- "text/plain": [
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- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
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- "source": [
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- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
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- "text/plain": [
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- "execution_count": 6,
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- "source": [
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diff --git a/info4/kapitel-2/Minimalautomat.ipynb b/info4/kapitel-2/Minimalautomat.ipynb
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},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -590,7 +636,7 @@
"Executed operation: Markiere(z1,z0,0)"
]
},
- "execution_count": 9,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -601,7 +647,7 @@
},
{
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- "execution_count": 10,
+ "execution_count": 11,
"metadata": {},
"outputs": [
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]
},
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+ "execution_count": 11,
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}
@@ -815,7 +892,7 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 12,
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{
@@ -824,7 +901,7 @@
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]
},
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+ "execution_count": 12,
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}
@@ -835,7 +912,7 @@
},
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+ "execution_count": 13,
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]
},
- "execution_count": 12,
+ "execution_count": 13,
"metadata": {},
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}
@@ -1068,7 +1178,7 @@
},
{
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- "execution_count": 13,
+ "execution_count": 14,
"metadata": {},
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{
@@ -1077,7 +1187,7 @@
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]
},
- "execution_count": 13,
+ "execution_count": 14,
"metadata": {},
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}
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},
{
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+ "execution_count": 15,
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- "<text text-anchor=\"middle\" x=\"80.6378\" y=\"-31.5811\" font-family=\"Times,serif\" font-size=\"12.00\">1</text>\n",
+ "<g id=\"edge2\" class=\"edge\">\n",
+ "<title>3->0</title>\n",
+ "<path fill=\"none\" stroke=\"green\" d=\"M198.04,-68.67C166.16,-85.24 99.03,-127.9 62.73,-154.27\"/>\n",
+ "<polygon fill=\"green\" stroke=\"green\" points=\"60.58,-151.51 54.63,-160.28 64.75,-157.14 60.58,-151.51\"/>\n",
+ "<text text-anchor=\"middle\" x=\"126.38\" y=\"-114.87\" font-family=\"Times,serif\" font-size=\"12.00\">1</text>\n",
"</g>\n",
"<!-- 3->0 -->\n",
- "<g id=\"edge14\" class=\"edge\"><title>3->0</title>\n",
- "<path fill=\"none\" stroke=\"red\" d=\"M110.204,-28.2522C95.5439,-34.8253 72.7956,-42.5978 54.0656,-47.6362\"/>\n",
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+ "<g id=\"edge7\" class=\"edge\">\n",
+ "<title>3->0</title>\n",
+ "<path fill=\"none\" stroke=\"red\" d=\"M202.37,-75.43C174.03,-97.5 107.26,-140.74 68.16,-162.73\"/>\n",
+ "<polygon fill=\"red\" stroke=\"red\" points=\"66.4,-159.71 59.32,-167.59 69.77,-165.84 66.4,-159.71\"/>\n",
+ "<text text-anchor=\"middle\" x=\"139.26\" y=\"-122.48\" font-family=\"Times,serif\" font-size=\"12.00\">0</text>\n",
"</g>\n",
"<!-- 3->4 -->\n",
- "<g id=\"edge22\" class=\"edge\"><title>3->4</title>\n",
- "<path fill=\"none\" stroke=\"purple\" stroke-width=\"2\" d=\"M120.93,-35.8022C117.934,-66.3794 117.659,-129.101 120.105,-165.581\"/>\n",
- "<polygon fill=\"purple\" stroke=\"purple\" points=\"116.652,-166.312 120.951,-175.996 123.629,-165.745 116.652,-166.312\"/>\n",
- "<text text-anchor=\"middle\" x=\"125.517\" y=\"-97.0916\" font-family=\"Times,serif\" font-size=\"12.00\">↔</text>\n",
+ "<g id=\"edge11\" class=\"edge\">\n",
+ "<title>3->4</title>\n",
+ "<path fill=\"none\" stroke=\"purple\" stroke-width=\"2\" d=\"M213.08,-80.63C207.67,-166.27 207.49,-524.74 212.52,-629.18\"/>\n",
+ "<polygon fill=\"purple\" stroke=\"purple\" stroke-width=\"2\" points=\"209.04,-629.49 213.08,-639.29 216.03,-629.11 209.04,-629.49\"/>\n",
+ "<text text-anchor=\"middle\" x=\"207.8\" y=\"-358.31\" font-family=\"Times,serif\" font-size=\"12.00\">↔</text>\n",
"</g>\n",
"<!-- 4->1 -->\n",
- "<g id=\"edge6\" class=\"edge\"><title>4->1</title>\n",
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+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>4->1</title>\n",
+ "<path fill=\"none\" stroke=\"green\" d=\"M202.37,-644.57C174.03,-622.5 107.26,-579.26 68.16,-557.27\"/>\n",
+ "<polygon fill=\"green\" stroke=\"green\" points=\"69.77,-554.16 59.32,-552.41 66.4,-560.29 69.77,-554.16\"/>\n",
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"</g>\n",
"<!-- 4->1 -->\n",
- "<g id=\"edge16\" class=\"edge\"><title>4->1</title>\n",
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+ "<g id=\"edge8\" class=\"edge\">\n",
+ "<title>4->1</title>\n",
+ "<path fill=\"none\" stroke=\"red\" d=\"M198.04,-651.33C166.16,-634.76 99.03,-592.1 62.73,-565.73\"/>\n",
+ "<polygon fill=\"red\" stroke=\"red\" points=\"64.75,-562.86 54.63,-559.72 60.58,-568.49 64.75,-562.86\"/>\n",
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"</g>\n",
"<!-- 4->3 -->\n",
- "<g id=\"edge24\" class=\"edge\"><title>4->3</title>\n",
- "<path fill=\"none\" stroke=\"purple\" stroke-width=\"2\" d=\"M129.481,-175.782C132.477,-145.204 132.753,-82.4832 130.307,-46.0027\"/>\n",
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- "<text text-anchor=\"middle\" x=\"124.894\" y=\"-107.292\" font-family=\"Times,serif\" font-size=\"12.00\">↔</text>\n",
+ "<g id=\"edge12\" class=\"edge\">\n",
+ "<title>4->3</title>\n",
+ "<path fill=\"none\" stroke=\"purple\" stroke-width=\"2\" d=\"M218.18,-639.37C223.59,-553.73 223.78,-195.26 218.74,-90.82\"/>\n",
+ "<polygon fill=\"purple\" stroke=\"purple\" stroke-width=\"2\" points=\"222.23,-90.51 218.18,-80.71 215.24,-90.89 222.23,-90.51\"/>\n",
+ "<text text-anchor=\"middle\" x=\"223.46\" y=\"-368.49\" font-family=\"Times,serif\" font-size=\"12.00\">↔</text>\n",
"</g>\n",
"<!-- 5 -->\n",
- "<g id=\"node6\" class=\"node\"><title>5</title>\n",
+ "<g id=\"node6\" class=\"node\">\n",
+ "<title>5</title>\n",
"</g>\n",
"<!-- 5->2 -->\n",
- "<g id=\"edge30\" class=\"edge\"><title>5->2</title>\n",
- "<path fill=\"none\" stroke=\"black\" d=\"M260.938,-105.792C247.476,-105.792 231.204,-105.792 217.542,-105.792\"/>\n",
- "<polygon fill=\"black\" stroke=\"black\" points=\"217.249,-102.292 207.249,-105.792 217.249,-109.292 217.249,-102.292\"/>\n",
+ "<g id=\"edge15\" class=\"edge\">\n",
+ "<title>5->2</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M466.87,-360C436.03,-360 385.87,-360 354.26,-360\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"353.92,-356.5 343.92,-360 353.92,-363.5 353.92,-356.5\"/>\n",
"</g>\n",
"</g>\n",
"</svg>"
@@ -1231,7 +1362,7 @@
"<Dot visualization: custom_graph []>"
]
},
- "execution_count": 14,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -1286,9 +1417,23 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 16,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{\\{\\mathit{z0}\\},\\{\\mathit{z1},\\mathit{z2}\\},\\{\\mathit{z3},\\mathit{z4}\\}\\}$"
+ ],
+ "text/plain": [
+ "{{z0},{z1,z2},{z3,z4}}"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":let ZF {zs| #x.(x:Z & closure(fusioniert)[{x}] = zs)}"
]
@@ -1302,7 +1447,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -1314,7 +1459,7 @@
"{({z0}↦0↦{z1,z2}),({z0}↦1↦{z1,z2}),({z1,z2}↦0↦{z3,z4}),({z1,z2}↦1↦{z3,z4}),({z3,z4}↦0↦{z3,z4}),({z3,z4}↦1↦{z3,z4})}"
]
},
- "execution_count": 32,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -1325,7 +1470,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -1335,7 +1480,7 @@
"Preference changed: DOT_ENGINE = dot\n"
]
},
- "execution_count": 33,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -1346,7 +1491,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -1355,64 +1500,73 @@
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
" -->\n",
"<!-- Title: state Pages: 1 -->\n",
- "<svg width=\"270pt\" height=\"116pt\"\n",
- " viewBox=\"0.00 0.00 270.00 116.02\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112.016)\">\n",
+ "<svg width=\"136pt\" height=\"218pt\"\n",
+ " viewBox=\"0.00 0.00 136.00 218.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 214)\">\n",
"<title>state</title>\n",
- "<polygon fill=\"white\" stroke=\"white\" points=\"-4,5 -4,-112.016 267,-112.016 267,5 -4,5\"/>\n",
+ "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-214 132,-214 132,4 -4,4\"/>\n",
"<!-- \\{z3,z4\\} -->\n",
- "<g id=\"node1\" class=\"node\"><title>\\{z3,z4\\}</title>\n",
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- "<text text-anchor=\"middle\" x=\"232\" y=\"-17.8157\" font-family=\"Times,serif\" font-size=\"14.00\">{z3,z4}</text>\n",
+ "<g id=\"node1\" class=\"node\">\n",
+ "<title>\\{z3,z4\\}</title>\n",
+ "<polygon fill=\"#cae1ff\" stroke=\"#cae1ff\" points=\"72,-36 0,-36 0,0 72,0 72,-36\"/>\n",
+ "<text text-anchor=\"middle\" x=\"36\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">{z3,z4}</text>\n",
"</g>\n",
"<!-- \\{z3,z4\\}->\\{z3,z4\\} -->\n",
- "<g id=\"edge2\" class=\"edge\"><title>\\{z3,z4\\}->\\{z3,z4\\}</title>\n",
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+ "<g id=\"edge1\" class=\"edge\">\n",
+ "<title>\\{z3,z4\\}->\\{z3,z4\\}</title>\n",
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"</g>\n",
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+ "<path fill=\"none\" stroke=\"sienna\" d=\"M72.31,-25.6C91.08,-26.77 108,-24.23 108,-18 108,-12.93 96.83,-10.31 82.57,-10.13\"/>\n",
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"</g>\n",
"<!-- \\{z1,z2\\} -->\n",
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- "<text text-anchor=\"middle\" x=\"128\" y=\"-17.8157\" font-family=\"Times,serif\" font-size=\"14.00\">{z1,z2}</text>\n",
+ "<g id=\"node2\" class=\"node\">\n",
+ "<title>\\{z1,z2\\}</title>\n",
+ "<polygon fill=\"#cae1ff\" stroke=\"#cae1ff\" points=\"72,-123 0,-123 0,-87 72,-87 72,-123\"/>\n",
+ "<text text-anchor=\"middle\" x=\"36\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">{z1,z2}</text>\n",
"</g>\n",
"<!-- \\{z1,z2\\}->\\{z3,z4\\} -->\n",
- "<g id=\"edge4\" class=\"edge\"><title>\\{z1,z2\\}->\\{z3,z4\\}</title>\n",
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+ "<g id=\"edge2\" class=\"edge\">\n",
+ "<title>\\{z1,z2\\}->\\{z3,z4\\}</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M26.35,-86.61C22.19,-77.08 18.74,-65.01 21,-54 21.55,-51.3 22.33,-48.55 23.23,-45.84\"/>\n",
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"</g>\n",
"<!-- \\{z1,z2\\}->\\{z3,z4\\} -->\n",
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+ "<g id=\"edge5\" class=\"edge\">\n",
+ "<title>\\{z1,z2\\}->\\{z3,z4\\}</title>\n",
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"</g>\n",
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- "<text text-anchor=\"middle\" x=\"27\" y=\"-17.8157\" font-family=\"Times,serif\" font-size=\"14.00\">{z0}</text>\n",
+ "<g id=\"node3\" class=\"node\">\n",
+ "<title>\\{z0\\}</title>\n",
+ "<polygon fill=\"#cae1ff\" stroke=\"#cae1ff\" points=\"63,-210 9,-210 9,-174 63,-174 63,-210\"/>\n",
+ "<text text-anchor=\"middle\" x=\"36\" y=\"-188.3\" font-family=\"Times,serif\" font-size=\"14.00\">{z0}</text>\n",
"</g>\n",
"<!-- \\{z0\\}->\\{z1,z2\\} -->\n",
- "<g id=\"edge6\" class=\"edge\"><title>\\{z0\\}->\\{z1,z2\\}</title>\n",
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- "<text text-anchor=\"middle\" x=\"76\" y=\"-26.2157\" font-family=\"Times,serif\" font-size=\"14.00\">1</text>\n",
+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>\\{z0\\}->\\{z1,z2\\}</title>\n",
+ "<path fill=\"none\" stroke=\"firebrick\" d=\"M26.35,-173.61C22.19,-164.08 18.74,-152.01 21,-141 21.55,-138.3 22.33,-135.55 23.23,-132.84\"/>\n",
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"</g>\n",
"<!-- \\{z0\\}->\\{z1,z2\\} -->\n",
- "<g id=\"edge12\" class=\"edge\"><title>\\{z0\\}->\\{z1,z2\\}</title>\n",
- "<path fill=\"none\" stroke=\"sienna\" d=\"M54.3169,-7.29102C59.9867,-4.77625 66.0641,-2.54804 72,-1.21569 77.4162,-0 83.0129,-0.239126 88.469,-1.3699\"/>\n",
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+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>\\{z0\\}->\\{z1,z2\\}</title>\n",
+ "<path fill=\"none\" stroke=\"sienna\" d=\"M36,-173.8C36,-162.16 36,-146.55 36,-133.24\"/>\n",
+ "<polygon fill=\"sienna\" stroke=\"sienna\" points=\"39.5,-133.18 36,-123.18 32.5,-133.18 39.5,-133.18\"/>\n",
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"</g>\n",
"</g>\n",
"</svg>"
@@ -1421,7 +1575,7 @@
"<Dot visualization: expr_as_graph [δFZFδF={(({z0},0),{z1,z2}),(({z0},1),{z1,z2}),(({z1,z2},0),{z3,z4}),(({z1,z2},1),{z3,z4}),(({z3,z4},0),{z3,z4}),(({z3,z4},1),{z3,z4})} & ZF={{z0},{z1,z2},{z3,z4}}(\"0\",{a,b|a:ZF & b=δF(a, 0)})]>"
]
},
- "execution_count": 34,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -1432,7 +1586,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -1457,7 +1611,7 @@
"{z3,z4}\t1\t{z3,z4}\n"
]
},
- "execution_count": 35,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -1466,31 +1620,6 @@
":table δF"
]
},
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "ProB 2 Jupyter kernel: 1.1.1-SNAPSHOT (e52e0cac2096ac02eac65e556edce9dcd142d920)\n",
- "ProB 2: 3.10.0 (0ee5d5eea6894b2899690565dfc3d9042098ce89)\n",
- "ProB CLI:\n",
- "\t1.10.0-nightly (05b24c45455b15cf94ea1daf18d2189efafa22fa)\n",
- "\tLast changed: Tue May 19 11:43:24 2020 +0200\n",
- "\tProlog: SICStus 4.5.1 (x86_64-darwin-17.7.0): Tue Apr 2 15:34:32 CEST 2019"
- ]
- },
- "execution_count": 36,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- ":version"
- ]
- },
{
"cell_type": "code",
"execution_count": null,
diff --git a/info4/kapitel-2/NFA_nach_DFA.ipynb b/info4/kapitel-2/NFA_nach_DFA.ipynb
index 55f2a267a5c4933c7b0c25393fb50a2e754fbe89..9735e0c4795eb6880dde63d60e5bb616b9acb1fe 100644
--- a/info4/kapitel-2/NFA_nach_DFA.ipynb
+++ b/info4/kapitel-2/NFA_nach_DFA.ipynb
@@ -100,7 +100,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Die Übergangsfunktion $\\delta$ gibt us für einen Zustand und ein Symbol die möglichen nächsten Zustände an."
+ "Die Überführungsfunktion $\\delta$ gibt uns für einen Zustand und ein Symbol die möglichen nächsten Zustände an."
]
},
{
diff --git a/info4/kapitel-3/CYK_Algorithmus.ipynb b/info4/kapitel-3/CYK_Algorithmus.ipynb
index 79917a0d46eb43a2b5b0bce6d2178d87be24db1a..d83a945820f7dc73e07cc04a00340a21e41f4dff 100644
--- a/info4/kapitel-3/CYK_Algorithmus.ipynb
+++ b/info4/kapitel-3/CYK_Algorithmus.ipynb
@@ -9,7 +9,7 @@
},
{
"cell_type": "code",
- "execution_count": 74,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -18,7 +18,7 @@
"Loaded machine: CYK"
]
},
- "execution_count": 74,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -79,7 +79,7 @@
},
{
"cell_type": "code",
- "execution_count": 75,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -88,7 +88,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 75,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -99,7 +99,7 @@
},
{
"cell_type": "code",
- "execution_count": 76,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -108,7 +108,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 76,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -126,7 +126,7 @@
},
{
"cell_type": "code",
- "execution_count": 77,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -138,7 +138,7 @@
"{(1↦b),(2↦a),(3↦a),(4↦b),(5↦a)}"
]
},
- "execution_count": 77,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -152,12 +152,12 @@
"metadata": {},
"source": [
"Am Anfang werden die Werte für T(i,0) in der INITIALISATION der Maschine berechnet:\n",
- "* for(i =1,2,...,n){T(i,0)={A∈N | A→x(i) ist Regel in P};"
+ "* for(i =1,2,...,n){T(i,0)={A∈N | A→x(i) ist Regel in P};}"
]
},
{
"cell_type": "code",
- "execution_count": 78,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -184,7 +184,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 78,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -195,7 +195,7 @@
},
{
"cell_type": "code",
- "execution_count": 79,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -207,7 +207,7 @@
"{S,A,B,C}"
]
},
- "execution_count": 79,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -218,7 +218,7 @@
},
{
"cell_type": "code",
- "execution_count": 59,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -230,7 +230,7 @@
"{({(1↦S)}↦{(1↦A),(2↦B)}),({(1↦S)}↦{(1↦B),(2↦C)}),({(1↦A)}↦{(1↦a)}),({(1↦A)}↦{(1↦B),(2↦A)}),({(1↦B)}↦{(1↦b)}),({(1↦B)}↦{(1↦C),(2↦C)}),({(1↦C)}↦{(1↦a)}),({(1↦C)}↦{(1↦A),(2↦B)})}"
]
},
- "execution_count": 59,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -241,7 +241,7 @@
},
{
"cell_type": "code",
- "execution_count": 56,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -253,7 +253,7 @@
"(1↦1)"
]
},
- "execution_count": 56,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -264,7 +264,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -273,7 +273,7 @@
"Executed operation: For_k_loop(1,1,{S,A})"
]
},
- "execution_count": 22,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -284,7 +284,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -296,7 +296,7 @@
"(2↦1)"
]
},
- "execution_count": 23,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -307,7 +307,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -341,7 +341,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 24,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -352,7 +352,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -361,7 +361,7 @@
"Executed operation: For_k_loop(2,1,{B})"
]
},
- "execution_count": 25,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -372,7 +372,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -384,7 +384,7 @@
"(3↦1)"
]
},
- "execution_count": 26,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -395,7 +395,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -429,7 +429,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 27,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -440,7 +440,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -452,7 +452,7 @@
"{(1↦0↦{B}),(1↦1↦{S,A}),(2↦0↦{A,C}),(2↦1↦{B}),(3↦0↦{A,C}),(4↦0↦{B}),(5↦0↦{A,C})}"
]
},
- "execution_count": 28,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -463,7 +463,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -472,7 +472,7 @@
"Executed operation: For_k_loop(3,1,{S,C})"
]
},
- "execution_count": 29,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -483,7 +483,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -492,7 +492,7 @@
"Executed operation: For_k_loop(4,1,{S,A})"
]
},
- "execution_count": 30,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -503,7 +503,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -537,7 +537,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 31,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -548,7 +548,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -557,7 +557,7 @@
"Executed operation: For_k_loop(1,2,{})"
]
},
- "execution_count": 32,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -568,7 +568,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -580,7 +580,7 @@
"(2↦2)"
]
},
- "execution_count": 33,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -591,7 +591,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
@@ -632,7 +632,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 34,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -643,7 +643,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
@@ -652,7 +652,7 @@
"Executed operation: For_k_loop(2,2,{B})"
]
},
- "execution_count": 35,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -663,7 +663,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -672,7 +672,7 @@
"Executed operation: For_k_loop(3,2,{B})"
]
},
- "execution_count": 36,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -683,7 +683,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
@@ -724,7 +724,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 37,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -735,7 +735,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -744,7 +744,7 @@
"Executed operation: For_k_loop(1,3,{})"
]
},
- "execution_count": 38,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -755,7 +755,7 @@
},
{
"cell_type": "code",
- "execution_count": 39,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -803,7 +803,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 39,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -814,7 +814,7 @@
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -823,7 +823,7 @@
"Executed operation: For_k_loop(2,3,{S,A,C})"
]
},
- "execution_count": 40,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -834,7 +834,7 @@
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -882,7 +882,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 41,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -893,7 +893,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -902,7 +902,7 @@
"Executed operation: For_k_loop(1,4,{S,A,C})"
]
},
- "execution_count": 42,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -913,7 +913,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -968,7 +968,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 43,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -979,7 +979,7 @@
},
{
"cell_type": "code",
- "execution_count": 46,
+ "execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -991,7 +991,7 @@
"TRUE"
]
},
- "execution_count": 46,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -1002,7 +1002,7 @@
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 32,
"metadata": {},
"outputs": [
{
@@ -1011,7 +1011,7 @@
"Executed operation: TRUE <-- Accept()"
]
},
- "execution_count": 47,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -1022,7 +1022,7 @@
},
{
"cell_type": "code",
- "execution_count": 48,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -1034,7 +1034,7 @@
"(1↦5↦5)"
]
},
- "execution_count": 48,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
diff --git a/info4/kapitel-3/PDA_nach_kfG.ipynb b/info4/kapitel-3/PDA_nach_kfG.ipynb
index d6615951606f9375ce7b0abc7969733a4ecc1d08..d21054f911344d2bcac989bef5a65be320b1a51f 100644
--- a/info4/kapitel-3/PDA_nach_kfG.ipynb
+++ b/info4/kapitel-3/PDA_nach_kfG.ipynb
@@ -158,7 +158,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Die Grammatik startet mit dem Startsymbol und simuliert die Ausführung eines entsprechenden PDAs. Dabei gibt es teils mehrere Wege, aber das Wort ab wird von mindestens einem erreicht."
+ "Die Grammatik startet mit dem Startsymbol und simuliert die Ausführung eines entsprechenden PDAs. Dabei gibt es teils mehrere Wege, aber das Wort $ab$ wird von mindestens einem erreicht."
]
},
{
diff --git a/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb b/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb
index 6f7bacbe4308cb6c6b1ed3111b8c03e256d8ce7d..29af86cbcd2e4e90a4cd906ab3e9c10e8bac4dc6 100644
--- a/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb
+++ b/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb
@@ -39,7 +39,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -48,7 +48,7 @@
"Loaded machine: TuringMachine_2"
]
},
- "execution_count": 13,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -113,7 +113,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -122,7 +122,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 14,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -133,7 +133,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -142,7 +142,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 15,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -160,7 +160,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -181,7 +181,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 16,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -192,7 +192,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -201,7 +201,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 17,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -212,7 +212,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -233,7 +233,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 18,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -244,7 +244,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -253,7 +253,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 19,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -264,7 +264,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -285,7 +285,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 20,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -296,7 +296,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -305,7 +305,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 21,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -316,7 +316,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -337,7 +337,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 22,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -348,7 +348,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -357,7 +357,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 23,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -368,7 +368,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -389,7 +389,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 24,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -400,7 +400,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -409,7 +409,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 25,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -420,7 +420,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -441,7 +441,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 26,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -452,7 +452,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -461,7 +461,7 @@
"Executed operation: GoTo(z0,Blank,z1,Blank,L)"
]
},
- "execution_count": 28,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -472,7 +472,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -494,7 +494,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 29,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -505,7 +505,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -514,7 +514,7 @@
"Executed operation: GoTo(z1,I,z1,O,L)"
]
},
- "execution_count": 30,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -525,7 +525,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -547,7 +547,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 31,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -558,7 +558,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -567,7 +567,7 @@
"Executed operation: GoTo(z1,I,z1,O,L)"
]
},
- "execution_count": 33,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -578,7 +578,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -600,7 +600,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 34,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -611,7 +611,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
@@ -620,7 +620,7 @@
"Executed operation: GoTo(z1,I,z1,O,L)"
]
},
- "execution_count": 35,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -631,7 +631,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
@@ -653,7 +653,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 36,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -664,7 +664,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -673,7 +673,7 @@
"Executed operation: GoTo(z1,I,z1,O,L)"
]
},
- "execution_count": 37,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -684,7 +684,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
@@ -706,7 +706,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 38,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -717,7 +717,7 @@
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -726,7 +726,7 @@
"Executed operation: GoTo(z1,I,z1,O,L)"
]
},
- "execution_count": 40,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -737,7 +737,7 @@
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -760,7 +760,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 41,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -771,7 +771,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -780,7 +780,7 @@
"Executed operation: GoTo(z1,Blank,ze,I,N)"
]
},
- "execution_count": 42,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -791,7 +791,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -814,7 +814,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 43,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -825,7 +825,7 @@
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -834,7 +834,7 @@
"Executed operation: Accept()"
]
},
- "execution_count": 44,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -852,7 +852,7 @@
},
{
"cell_type": "code",
- "execution_count": 46,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -875,7 +875,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 46,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -886,7 +886,7 @@
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -895,7 +895,7 @@
"Executed operation: GoTo(z0,I,z0,I,R)"
]
},
- "execution_count": 47,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -906,7 +906,7 @@
},
{
"cell_type": "code",
- "execution_count": 49,
+ "execution_count": 32,
"metadata": {},
"outputs": [
{
@@ -915,7 +915,7 @@
"Executed operation: GoTo(z0,O,z0,O,R)"
]
},
- "execution_count": 49,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -926,7 +926,7 @@
},
{
"cell_type": "code",
- "execution_count": 50,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -949,7 +949,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 50,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@@ -960,7 +960,7 @@
},
{
"cell_type": "code",
- "execution_count": 51,
+ "execution_count": 34,
"metadata": {},
"outputs": [
{
@@ -969,7 +969,7 @@
"Executed operation: GoTo(z0,O,z0,O,R)"
]
},
- "execution_count": 51,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -980,7 +980,7 @@
},
{
"cell_type": "code",
- "execution_count": 52,
+ "execution_count": 35,
"metadata": {},
"outputs": [
{
@@ -989,7 +989,7 @@
"Executed operation: GoTo(z0,O,z0,O,R)"
]
},
- "execution_count": 52,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -1000,7 +1000,7 @@
},
{
"cell_type": "code",
- "execution_count": 53,
+ "execution_count": 36,
"metadata": {},
"outputs": [
{
@@ -1009,7 +1009,7 @@
"Executed operation: GoTo(z0,O,z0,O,R)"
]
},
- "execution_count": 53,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -1020,7 +1020,7 @@
},
{
"cell_type": "code",
- "execution_count": 54,
+ "execution_count": 37,
"metadata": {},
"outputs": [
{
@@ -1029,7 +1029,7 @@
"Executed operation: GoTo(z0,O,z0,O,R)"
]
},
- "execution_count": 54,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -1040,7 +1040,7 @@
},
{
"cell_type": "code",
- "execution_count": 55,
+ "execution_count": 38,
"metadata": {},
"outputs": [
{
@@ -1049,7 +1049,7 @@
"Executed operation: GoTo(z0,Blank,z1,Blank,L)"
]
},
- "execution_count": 55,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
@@ -1060,7 +1060,7 @@
},
{
"cell_type": "code",
- "execution_count": 56,
+ "execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1083,7 +1083,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 56,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -1094,7 +1094,7 @@
},
{
"cell_type": "code",
- "execution_count": 58,
+ "execution_count": 40,
"metadata": {},
"outputs": [
{
@@ -1103,7 +1103,7 @@
"Executed operation: GoTo(z1,O,z2,I,L)"
]
},
- "execution_count": 58,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -1114,7 +1114,7 @@
},
{
"cell_type": "code",
- "execution_count": 59,
+ "execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -1137,7 +1137,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 59,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
@@ -1148,7 +1148,7 @@
},
{
"cell_type": "code",
- "execution_count": 60,
+ "execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -1157,7 +1157,7 @@
"Executed operation: GoTo(z2,O,z2,O,L)"
]
},
- "execution_count": 60,
+ "execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
@@ -1168,7 +1168,7 @@
},
{
"cell_type": "code",
- "execution_count": 61,
+ "execution_count": 43,
"metadata": {},
"outputs": [
{
@@ -1177,7 +1177,7 @@
"Executed operation: GoTo(z2,O,z2,O,L)"
]
},
- "execution_count": 61,
+ "execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
@@ -1188,7 +1188,7 @@
},
{
"cell_type": "code",
- "execution_count": 62,
+ "execution_count": 44,
"metadata": {},
"outputs": [
{
@@ -1197,7 +1197,7 @@
"Executed operation: GoTo(z2,O,z2,O,L)"
]
},
- "execution_count": 62,
+ "execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
@@ -1208,7 +1208,7 @@
},
{
"cell_type": "code",
- "execution_count": 63,
+ "execution_count": 45,
"metadata": {},
"outputs": [
{
@@ -1217,7 +1217,7 @@
"Executed operation: GoTo(z2,O,z2,O,L)"
]
},
- "execution_count": 63,
+ "execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
@@ -1228,7 +1228,7 @@
},
{
"cell_type": "code",
- "execution_count": 64,
+ "execution_count": 46,
"metadata": {},
"outputs": [
{
@@ -1237,7 +1237,7 @@
"Executed operation: GoTo(z2,I,z2,I,L)"
]
},
- "execution_count": 64,
+ "execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
@@ -1248,7 +1248,7 @@
},
{
"cell_type": "code",
- "execution_count": 65,
+ "execution_count": 47,
"metadata": {},
"outputs": [
{
@@ -1272,7 +1272,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 65,
+ "execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
@@ -1283,7 +1283,7 @@
},
{
"cell_type": "code",
- "execution_count": 66,
+ "execution_count": 48,
"metadata": {},
"outputs": [
{
@@ -1292,7 +1292,7 @@
"Executed operation: GoTo(z2,Blank,ze,Blank,R)"
]
},
- "execution_count": 66,
+ "execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
@@ -1303,7 +1303,7 @@
},
{
"cell_type": "code",
- "execution_count": 67,
+ "execution_count": 49,
"metadata": {},
"outputs": [
{
@@ -1327,7 +1327,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 67,
+ "execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
@@ -1340,12 +1340,12 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Die Turing Maschine at 33 als Ergebnis zurückgegeben."
+ "Die Turing Maschine hat 33 als Ergebnis zurückgegeben."
]
},
{
"cell_type": "code",
- "execution_count": 68,
+ "execution_count": 50,
"metadata": {},
"outputs": [
{
@@ -1354,7 +1354,7 @@
"Executed operation: Accept()"
]
},
- "execution_count": 68,
+ "execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}