diff --git a/info4/kapitel-1/Grammatiken.ipynb b/info4/kapitel-1/Grammatiken.ipynb
index c136d3c456810956405a70c5a7d2e57c1c577b70..1ed187c67de310e6051920a1f79d8057a39d7df1 100644
--- a/info4/kapitel-1/Grammatiken.ipynb
+++ b/info4/kapitel-1/Grammatiken.ipynb
@@ -29,7 +29,7 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -38,7 +38,7 @@
"Loaded machine: Grammatik"
]
},
- "execution_count": 1,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -65,7 +65,7 @@
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -74,7 +74,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 2,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -85,7 +85,7 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -103,7 +103,7 @@
"\tRHS = []"
]
},
- "execution_count": 3,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -121,7 +121,7 @@
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -133,13 +133,13 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 4,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "P[{[S]}]"
+ "P[{ [S] }]"
]
},
{
@@ -159,7 +159,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -168,7 +168,7 @@
"Loaded machine: Grammatik"
]
},
- "execution_count": 5,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -199,7 +199,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -208,7 +208,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 6,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -221,12 +221,35 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Da diese Relation unendlich ist wird diese im Notebook symbolisch gehalten. Wir können aber prüfen ob Paare an Folgen in der Relation sind:"
+ "Da diese Relation ```abl``` unendlich ist wird diese im Notebook symbolisch gehalten. Wir können aber prüfen ob Paare an Folgen in der Relation sind:"
]
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\newcommand{\\qdot}{\\mathord{\\mkern1mu\\cdot\\mkern1mu}}/*@symbolic*/ \\{\\mathit{u},\\mathit{v}\\mid\\exists(\\mathit{x},\\mathit{z},\\mathit{p},\\mathit{q})\\qdot(\\mathit{p} \\mapsto \\mathit{q} \\in \\{([S]\\mapsto []),([S]\\mapsto [a,\\mathit{S},b])\\} \\land \\mathit{u} = \\mathit{x} ⌒ \\mathit{p} ⌒ \\mathit{z} \\land \\mathit{v} = \\mathit{x} ⌒ \\mathit{q} ⌒ \\mathit{z})\\}$"
+ ],
+ "text/plain": [
+ "/*@symbolic*/ {u,v∣∃(x,z,p,q)·(p ↦ q ∈ {([S]↦[]),([S]↦[a,S,b])} ∧ u = x ⌒ p ⌒ z ∧ v = x ⌒ q ⌒ z)}"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "abl"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -238,18 +261,18 @@
"TRUE"
]
},
- "execution_count": 7,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "[S] ↦ [a,S,b] ∈ abl"
+ "[a,S,b,S] ↦ [a,S,b,a,S,b] ∈ abl"
]
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -261,7 +284,7 @@
"FALSE"
]
},
- "execution_count": 8,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -272,7 +295,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -290,13 +313,13 @@
"\tx = []"
]
},
- "execution_count": 9,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "[S] ↦ x : abl"
+ "[S] ↦ x ∈ abl"
]
},
{
@@ -308,7 +331,7 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -320,36 +343,36 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 10,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "abl[ {[S]} ]"
+ "abl[ { [S] } ]"
]
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
- "$\\{[a,b],[a,\\mathit{a},\\mathit{S},\\mathit{b},b]\\}$"
+ "$\\{[a,\\mathit{b},S],[a,\\mathit{S},b],[a,\\mathit{S},\\mathit{b},\\mathit{a},\\mathit{S},b],[a,\\mathit{a},\\mathit{S},\\mathit{b},\\mathit{b},S]\\}$"
],
"text/plain": [
- "{[a,b],[a,a,S,b,b]}"
+ "{[a,b,S],[a,S,b],[a,S,b,a,S,b],[a,a,S,b,b,S]}"
]
},
- "execution_count": 11,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "abl[ {[a,S,b]} ]"
+ "abl[ {[a,S,b,S]} ]"
]
},
{
@@ -361,7 +384,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -373,7 +396,7 @@
"{[a,b],[a,a,S,b,b]}"
]
},
- "execution_count": 12,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -384,7 +407,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -396,7 +419,7 @@
"{[a,a,b,b],[a,a,a,S,b,b,b]}"
]
},
- "execution_count": 13,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -420,7 +443,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -432,7 +455,7 @@
"TRUE"
]
},
- "execution_count": 14,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -450,7 +473,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
@@ -462,7 +485,7 @@
"{[S]}"
]
},
- "execution_count": 15,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -473,7 +496,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -485,7 +508,7 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 16,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -496,7 +519,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -508,7 +531,7 @@
"{[a,b],[a,a,S,b,b]}"
]
},
- "execution_count": 17,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -519,7 +542,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -531,7 +554,7 @@
"{[a,a,b,b],[a,a,a,S,b,b,b]}"
]
},
- "execution_count": 18,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -542,7 +565,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -554,7 +577,7 @@
"{[a,a,a,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 19,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -577,7 +600,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -589,7 +612,7 @@
"{[],[a,b],[S],[a,a,b,b],[a,S,b],[a,a,a,b,b,b],[a,a,S,b,b],[a,a,a,S,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 20,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -607,7 +630,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -619,7 +642,7 @@
"{[],[a,b],[a,a,b,b],[a,a,a,b,b,b]}"
]
},
- "execution_count": 21,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -637,7 +660,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -649,7 +672,7 @@
"{[],[a,b],[S],[a,a,b,b],[a,S,b],[a,a,a,b,b,b],[a,a,S,b,b],[a,a,a,S,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 22,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -660,7 +683,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 32,
"metadata": {},
"outputs": [
{
@@ -669,7 +692,7 @@
"Preference changed: DOT_DECOMPOSE_NODES = FALSE\n"
]
},
- "execution_count": 23,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -680,7 +703,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -797,7 +820,7 @@
"<Dot visualization: expr_as_graph [SFSF={[],[a,b],[S],[a,a,b,b],[a,S,b],[a,a,a,b,b,b],[a,a,S,b,b],[a,a,a,S,b,b,b],[a,a,a,a,S,b,b,b,b]}(\"abl\",SF<|abl|>SF)]>"
]
},
- "execution_count": 24,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@@ -815,7 +838,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 34,
"metadata": {},
"outputs": [
{
@@ -824,7 +847,7 @@
"Loaded machine: Grammatik2"
]
},
- "execution_count": 25,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -860,7 +883,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 35,
"metadata": {},
"outputs": [
{
@@ -869,7 +892,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 26,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -880,7 +903,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 36,
"metadata": {},
"outputs": [
{
@@ -892,7 +915,7 @@
"{[S],[a,b,c],[a,b,C],[a,S,B,C],[a,B,C],[a,a,b,c,B,C],[a,a,b,C,B,C],[a,a,b,B,C,C],[a,a,B,C,B,C],[a,a,B,B,C,C],[a,a,S,B,C,B,C],[a,a,S,B,B,C,C],[a,a,a,S,B,C,B,B,C,C],[a,a,a,S,B,B,C,C,B,C],[a,a,a,S,B,C,B,C,B,C],[a,a,a,B,B,C,C,B,C],[a,a,a,b,C,B,C,B,C],[a,a,a,B,C,B,B,C,C],[a,a,a,B,C,B,C,B,C],[a,a,a,a,B,C,B,C,B,C,B,C],[a,a,a,a,S,B,C,B,C,B,C,B,C]}"
]
},
- "execution_count": 27,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -903,7 +926,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 37,
"metadata": {},
"outputs": [
{
@@ -915,7 +938,7 @@
"{[a,b,c]}"
]
},
- "execution_count": 28,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -926,7 +949,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 38,
"metadata": {},
"outputs": [
{
@@ -935,7 +958,7 @@
"Preference changed: DOT_DECOMPOSE_NODES = FALSE\n"
]
},
- "execution_count": 29,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
@@ -946,7 +969,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1213,7 +1236,7 @@
"<Dot visualization: expr_as_graph [SFSF={[S],[a,b,c],[a,b,C],[a,S,B,C],[a,B,C],[a,a,b,c,B,C],[a,a,b,C,B,C],[a,a,b,B,C,C],[a,a,B,C,B,C],[a,a,B,B,C,C],[a,a,S,B,C,B,C],[a,a,S,B,B,C,C],[a,a,a,S,B,C,B,B,C,C],[a,a,a,S,B,B,C,C,B,C],[a,a,a,S,B,C,B,C,B,C],[a,a,a,B,B,C,C,B,C],[a,a,a,b,C,B,C,B,C],[a,a,a,B,C,B,B,C,C],[a,a,a,B,C,B,C,B,C],[a,a,a,a,B,C,B,C,B,C,B,C],[a,a,a,a,S,B,C,B,C,B,C,B,C]}(\"abl\",SF<|abl|>SF)]>"
]
},
- "execution_count": 30,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -1224,7 +1247,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
@@ -1246,9 +1269,9 @@
"* $G$ ist eine __Typ-1-Grammatik__ (bzw. __kontextsensitiv__ bzw. _nichtverkürzend_ oder __monoton__), falls für alle Regeln $p \\rightarrow q$ in\n",
" $P$ gilt: $|p| \\leq |q|$.\n",
" \n",
- "* Eine Typ-1-Grammatik $G$ ist __vom Typ 2__ (bzw. ___kontextfrei__), falls für alle Regeln $p \\rightarrow q$ in $P$ gilt: $p \\in N$.\n",
+ "* Eine Typ-1-Grammatik $G$ ist __vom Typ 2__ (bzw. __kontextfrei__), falls für alle Regeln $p \\rightarrow q$ in $P$ gilt: $p \\in N$.\n",
" \n",
- "* Eine Typ-2-Grammatik $G$ ist __vom Typ 3__ (bzw. __regulär__ bzw. __rechtslinear__), falls f\"ur\n",
+ "* Eine Typ-2-Grammatik $G$ ist __vom Typ 3__ (bzw. __regulär__ bzw. __rechtslinear__), falls für\n",
" alle Regeln $p \\rightarrow q$ in $P$ gilt: $p \\in N$ und $q \\in \\Sigma \\cup \\Sigma N$.\n",
"\n",
"Eine Sprache $A \\subseteq \\Sigma^*$ ist genau dann vom Typ $i \\in\n",
@@ -1257,23 +1280,9 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/markdown": [
- "$\\{([a,B]\\mapsto [a,b]),([b,B]\\mapsto [b,b]),([b,C]\\mapsto [b,c]),([c,C]\\mapsto [c,c]),([S]\\mapsto [a,\\mathit{S},\\mathit{B},C]),([S]\\mapsto [a,\\mathit{B},C]),([C,B]\\mapsto [B,C])\\}$"
- ],
- "text/plain": [
- "{([a,B]↦[a,b]),([b,B]↦[b,b]),([b,C]↦[b,c]),([c,C]↦[c,c]),([S]↦[a,S,B,C]),([S]↦[a,B,C]),([C,B]↦[B,C])}"
- ]
- },
- "execution_count": 32,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"P"
]
@@ -1288,7 +1297,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -1300,7 +1309,7 @@
"TRUE"
]
},
- "execution_count": 33,
+ "execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
@@ -1309,6 +1318,29 @@
"∀(p,q).( p↦q ∈ P ⇒ size(p) ≤ size(q))"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{([a,B]\\mapsto [a,b]),([b,B]\\mapsto [b,b]),([b,C]\\mapsto [b,c]),([c,C]\\mapsto [c,c]),([S]\\mapsto [a,\\mathit{S},\\mathit{B},C]),([S]\\mapsto [a,\\mathit{B},C]),([C,B]\\mapsto [B,C])\\}$"
+ ],
+ "text/plain": [
+ "{([a,B]↦[a,b]),([b,B]↦[b,b]),([b,C]↦[b,c]),([c,C]↦[c,c]),([S]↦[a,S,B,C]),([S]↦[a,B,C]),([C,B]↦[B,C])}"
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "P"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -1318,7 +1350,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 43,
"metadata": {},
"outputs": [
{
@@ -1330,7 +1362,7 @@
"FALSE"
]
},
- "execution_count": 34,
+ "execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
@@ -1349,7 +1381,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 44,
"metadata": {},
"outputs": [
{
@@ -1376,7 +1408,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 45,
"metadata": {},
"outputs": [
{
@@ -1388,7 +1420,7 @@
"{([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 36,
+ "execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
@@ -1399,7 +1431,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 46,
"metadata": {},
"outputs": [
{
@@ -1417,7 +1449,7 @@
"\tP1 = {([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 37,
+ "execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
@@ -1435,7 +1467,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 47,
"metadata": {},
"outputs": [
{
@@ -1447,7 +1479,7 @@
"FALSE"
]
},
- "execution_count": 38,
+ "execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
@@ -1458,7 +1490,7 @@
},
{
"cell_type": "code",
- "execution_count": 39,
+ "execution_count": 48,
"metadata": {},
"outputs": [
{
@@ -1480,7 +1512,7 @@
"\tP1 = {([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 39,
+ "execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}