From c5ed660943bd41a88f481f199adaa7be5bf0a1aa Mon Sep 17 00:00:00 2001
From: Chris <Christopher.Happe@uni-duesseldorf.de>
Date: Sat, 31 Oct 2020 11:21:27 +0100
Subject: [PATCH] =?UTF-8?q?Visualisierung=20komplexer=20Automaten=20=C3=BC?=
=?UTF-8?q?berarbeitet?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
---
info4/kapitel-2/Abschlusseigenschaften.ipynb | 672 +++++++++++++------
info4/kapitel-2/img/konkatenation_M1.svg | 1 +
info4/kapitel-2/img/konkatenation_M2.svg | 1 +
3 files changed, 486 insertions(+), 188 deletions(-)
create mode 100644 info4/kapitel-2/img/konkatenation_M1.svg
create mode 100644 info4/kapitel-2/img/konkatenation_M2.svg
diff --git a/info4/kapitel-2/Abschlusseigenschaften.ipynb b/info4/kapitel-2/Abschlusseigenschaften.ipynb
index 2e37762..85fa82c 100644
--- a/info4/kapitel-2/Abschlusseigenschaften.ipynb
+++ b/info4/kapitel-2/Abschlusseigenschaften.ipynb
@@ -609,6 +609,22 @@
":constants"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<table align=\"LEFT\">\n",
+ " <tr>\n",
+ " <td width=50%>Der Automat $M_1$</td>\n",
+ " <td width=50%>Der Automat $M_2$</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td width=50%><img src=\"./img/konkatenation_M1.svg\" width=100%></td>\n",
+ " <td width=50%><img src=\"./img/konkatenation_M2.svg\" width=100%></td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 9,
@@ -1081,7 +1097,7 @@
"MACHINE NFA\n",
"SETS\n",
" Z = {z10,z11, z12, z20,z21,z22}\n",
- "CONSTANTS Σ, M, Z_gesamt, δ, S, F, f,\n",
+ "CONSTANTS Σ, M, Z_gesamt, δ, S, F,\n",
" M1, Z1, δ1, S1, F1,\n",
" M2, Z2, δ2, S2, F2\n",
" \n",
@@ -1103,16 +1119,16 @@
" (z11,0)↦{z12}, (z11,1)↦{z11},\n",
" (z12,0)↦{z12}, (z12,1)↦{z11}} ∧\n",
" \n",
- " // Der Automat M2 (L(M2)={1^n|n∈ℕ_0}):\n",
+ " // Der Automat M2 (L(M2)={0^n|n∈ℕ_0}):\n",
" M2 = (Σ, Z2, δ2, S2, F2) ∧\n",
" Z2 ⊆ Z ∧\n",
" δ2 ∈ (Z2×Σ) → ℙ(Z2) ∧\n",
" S2 ⊆ Z2 ∧ F2 ⊆ Z2\n",
" ∧\n",
" Z2 = {z20,z21,z22} ∧\n",
- " S2 = {z20, z21} ∧ F2 = {z20, z21} ∧\n",
- " δ2 = { (z20,0)↦{z22}, (z20,1)↦{z21},\n",
- " (z21,0)↦{z22}, (z21,1)↦{z21},\n",
+ " S2 = {z20} ∧ F2 = {z20, z21} ∧\n",
+ " δ2 = { (z20,0)↦{z21}, (z20,1)↦{z22},\n",
+ " (z21,0)↦{z21}, (z21,1)↦{z22},\n",
" (z22,0)↦{z22}, (z22,1)↦{z22}} ∧\n",
"\n",
" //Der Automat nach \"Grundkurs Theoretische Informatik\"\n",
@@ -1124,15 +1140,17 @@
" ∃zustand1,zustand2,symbol,menge.(\n",
" x=((zustand1, zustand2), symbol)↦menge ∧\n",
" zustand1∈Z1 ∧ zustand2∈Z2 ∧ symbol∈Σ ∧\n",
- " menge = δ1(zustand1, symbol)*δ2(zustand2, symbol))} ∧\n",
- " \n",
- " //Eine Hilfsfunktion zur Visualisierung\n",
- " f ∈ seq(Z_gesamt) ∧ ran(f) = Z_gesamt \n",
+ " menge = δ1(zustand1, symbol)*δ2(zustand2, symbol))}\n",
+ "\n",
"DEFINITIONS // Für den Zustandsgraphen:\n",
- " ANIMATION_FUNCTION1 == {r,c,i| r∈dom(f) ∧ c=0 ∧ i=f(r)};\n",
- " ANIMATION_FUNCTION2 == {(0,0,\"Zustand\"),(0,1,\"δ(Zustand,0)\"),(0,2,\"δ(Zustand,1)\")};\n",
- " ANIMATION_FUNCTION3 == {r,c,i| r∈dom(f) ∧ c=1 ∧ i=δ(f(r), 0)};\n",
- " ANIMATION_FUNCTION4 == {r,c,i| r∈dom(f) ∧ c=2 ∧ i=δ(f(r), 1)};\n",
+ " \"LibraryStrings.def\";\n",
+ " CUSTOM_GRAPH_NODES1 == rec(shape:\"doublecircle\",nodes:{x | ∃y.(x=TO_STRING(y) ∧ y:F)}); //Endzustände\n",
+ " CUSTOM_GRAPH_NODES2 == rec(shape:\"circle\",nodes:{x | ∃y.(x=TO_STRING(y) ∧ y:Z_gesamt\\F)}); // andere Zustände\n",
+ " CUSTOM_GRAPH_NODES3 == rec(shape:\"none\",color:\"white\",style:\"none\",nodes:{\"\"});\n",
+ " CUSTOM_GRAPH_EDGES1 == rec(color:\"black\",label:\"\",edges:{\"\"}*{x | ∃y.(x=TO_STRING(y) ∧ y:S)}); // Kanten für Startknoten\n",
+ " CUSTOM_GRAPH_EDGES2 == rec(color:\"green\",label:\"0\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,0) ∧ y∉δ(x,1) ∧ a=TO_STRING(x) ∧ b=TO_STRING(y))}); \n",
+ " CUSTOM_GRAPH_EDGES3 == rec(color:\"green\",label:\"1\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,1) ∧ y∉δ(x,0) ∧ a=TO_STRING(x) ∧ b=TO_STRING(y))});\n",
+ " CUSTOM_GRAPH_EDGES4 == rec(color:\"green\",label:\"0, 1\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,0) ∧ y∈δ(x,1)∧ a=TO_STRING(x) ∧ b=TO_STRING(y))})\n",
"END"
]
},
@@ -1163,91 +1181,224 @@
"outputs": [
{
"data": {
- "text/plain": [
- "Machine initialised using operation 1: $initialise_machine()"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- ":init"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/markdown": [
- "<table style=\"font-family:monospace\"><tbody>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">Zustand</td>\n",
- "<td style=\"padding:10px\">δ(Zustand,0)</td>\n",
- "<td style=\"padding:10px\">δ(Zustand,1)</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "</tbody></table>"
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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 2.44.1 (0)\n",
+ " -->\n",
+ "<!-- Title: prob_graph Pages: 1 -->\n",
+ "<svg width=\"540pt\" height=\"719pt\"\n",
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+ "<g id=\"graph0\" class=\"graph\" transform=\"scale(0.73 0.73) rotate(0) translate(4 975.17)\">\n",
+ "<title>prob_graph</title>\n",
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+ "<!-- 0 -->\n",
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+ "</g>\n",
+ "<!-- 0->1 -->\n",
+ "<g id=\"edge3\" class=\"edge\">\n",
+ "<title>0->1</title>\n",
+ "<path fill=\"none\" stroke=\"green\" d=\"M70.51,-665.18C84.7,-611.39 106.5,-528.68 121.54,-471.66\"/>\n",
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+ "</g>\n",
+ "<!-- 2->6 -->\n",
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+ "<title>2->6</title>\n",
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+ "<g id=\"edge1\" class=\"edge\">\n",
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+ "<g id=\"edge12\" class=\"edge\">\n",
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+ "<!-- 9 -->\n",
+ "<g id=\"node10\" class=\"node\">\n",
+ "<title>9</title>\n",
+ "</g>\n",
+ "<!-- 9->2 -->\n",
+ "<g id=\"edge10\" class=\"edge\">\n",
+ "<title>9->2</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M183.32,-917.85C183.32,-888.9 183.32,-828.97 183.32,-782.8\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"186.82,-782.58 183.32,-772.58 179.82,-782.58 186.82,-782.58\"/>\n",
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],
"text/plain": [
- "<Animation function visualisation>"
+ "<Dot visualization: custom_graph []>"
]
},
- "execution_count": 16,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- ":show"
+ ":dot custom_graph"
]
},
{
@@ -1259,7 +1410,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -1268,7 +1419,7 @@
"Loaded machine: NFA"
]
},
- "execution_count": 17,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -1278,7 +1429,7 @@
"MACHINE NFA\n",
"SETS\n",
" Z = {z10,z11, z12, z20,z21,z22}\n",
- "CONSTANTS Σ, M, Z_gesamt, δ, S, F, f,\n",
+ "CONSTANTS Σ, M, Z_gesamt, δ, S, F,\n",
" M1, Z1, δ1, S1, F1,\n",
" M2, Z2, δ2, S2, F2\n",
" \n",
@@ -1299,16 +1450,16 @@
" (z11,0)↦{z12}, (z11,1)↦{z11},\n",
" (z12,0)↦{z12}, (z12,1)↦{z11}} ∧\n",
"\n",
- " // Der Automat M2 (L(M2)={1^n|n∈ℕ_0}):\n",
+ " // Der Automat M2 (L(M2)={0^n|n∈ℕ_0}):\n",
" M2 = (Σ, Z2, δ2, S2, F2) ∧\n",
" Z2 ⊆ Z ∧\n",
" δ2 ∈ (Z2×Σ) → ℙ(Z2) ∧\n",
" S2 ⊆ Z2 ∧ F2 ⊆ Z2 \n",
" ∧\n",
" Z2 = {z20,z21,z22} ∧\n",
- " S2 = {z20, z21} ∧ F2 = {z20, z21} ∧\n",
- " δ2 = { (z20,0)↦{z22}, (z20,1)↦{z21},\n",
- " (z21,0)↦{z22}, (z21,1)↦{z21},\n",
+ " S2 = {z20} ∧ F2 = {z20, z21} ∧\n",
+ " δ2 = { (z20,0)↦{z21}, (z20,1)↦{z22},\n",
+ " (z21,0)↦{z21}, (z21,1)↦{z22},\n",
" (z22,0)↦{z22}, (z22,1)↦{z22}} ∧\n",
"\n",
" //Eigene Konstruktion analog zu \"Grundkurs Theoretische Informatik\" (s.o.)\n",
@@ -1322,20 +1473,21 @@
" zustand1∈Z1 ∧ zustand2∈Z2 ∧ symbol∈Σ ∧\n",
" menge = δ1(zustand1, symbol)*δ2(zustand2, symbol))}\n",
" \n",
- " //Eine Hilfsfunktion zur Visualisierung\n",
- " ∧ f ∈ seq(Z_gesamt) ∧ ran(f) = Z_gesamt \n",
"DEFINITIONS // Für den Zustandsgraphen:\n",
" \"LibraryStrings.def\";\n",
- " ANIMATION_FUNCTION1 == {r,c,i| r∈dom(f) ∧ c=0 ∧ i=f(r)};\n",
- " ANIMATION_FUNCTION2 == {(0,0,\"Zustand\"),(0,1,\"δ(Zustand,0)\"),(0,2,\"δ(Zustand,1)\")};\n",
- " ANIMATION_FUNCTION3 == {r,c,i| r∈dom(f) ∧ c=1 ∧ i=δ(f(r), 0)};\n",
- " ANIMATION_FUNCTION4 == {r,c,i| r∈dom(f) ∧ c=2 ∧ i=δ(f(r), 1)};\n",
+ " CUSTOM_GRAPH_NODES1 == rec(shape:\"doublecircle\",nodes:{x | ∃y.(x=TO_STRING(y) ∧ y:F)}); //Endzustände\n",
+ " CUSTOM_GRAPH_NODES2 == rec(shape:\"circle\",nodes:{x | ∃y.(x=TO_STRING(y) ∧ y:Z_gesamt\\F)}); // andere Zustände\n",
+ " CUSTOM_GRAPH_NODES3 == rec(shape:\"none\",color:\"white\",style:\"none\",nodes:{\"\"});\n",
+ " CUSTOM_GRAPH_EDGES1 == rec(color:\"black\",label:\"\",edges:{\"\"}*{x | ∃y.(x=TO_STRING(y) ∧ y:S)}); // Kanten für Startknoten\n",
+ " CUSTOM_GRAPH_EDGES2 == rec(color:\"green\",label:\"0\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,0) ∧ y∉δ(x,1) ∧ a=TO_STRING(x) ∧ b=TO_STRING(y))}); \n",
+ " CUSTOM_GRAPH_EDGES3 == rec(color:\"green\",label:\"1\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,1) ∧ y∉δ(x,0) ∧ a=TO_STRING(x) ∧ b=TO_STRING(y))});\n",
+ " CUSTOM_GRAPH_EDGES4 == rec(color:\"green\",label:\"0, 1\",edges:{a,b|∃x,y.({(x,0),(x,1)} <:dom(δ) ∧ y∈δ(x,0) ∧ y∈δ(x,1)∧ a=TO_STRING(x) ∧ b=TO_STRING(y))})\n",
"END"
]
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -1344,7 +1496,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 18,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -1355,96 +1507,231 @@
},
{
"cell_type": "code",
- "execution_count": 19,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Machine initialised using operation 1: $initialise_machine()"
- ]
- },
- "execution_count": 19,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- ":init"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
- "text/markdown": [
- "<table style=\"font-family:monospace\"><tbody>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">Zustand</td>\n",
- "<td style=\"padding:10px\">δ(Zustand,0)</td>\n",
- "<td style=\"padding:10px\">δ(Zustand,1)</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z10|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z11|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z20)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z21)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z21)}</td>\n",
- "</tr>\n",
- "<tr>\n",
- "<td style=\"padding:10px\">(z12|->z22)</td>\n",
- "<td style=\"padding:10px\">{(z12|->z22)}</td>\n",
- "<td style=\"padding:10px\">{(z11|->z22)}</td>\n",
- "</tr>\n",
- "</tbody></table>"
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+ " -->\n",
+ "<!-- Title: prob_graph Pages: 1 -->\n",
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+ "</g>\n",
+ "<!-- 6 -->\n",
+ "<g id=\"node7\" class=\"node\">\n",
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+ "</g>\n",
+ "<!-- 6->3 -->\n",
+ "<g id=\"edge5\" class=\"edge\">\n",
+ "<title>6->3</title>\n",
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+ "<title>7->7</title>\n",
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+ "</g>\n",
+ "<!-- 7->8 -->\n",
+ "<g id=\"edge6\" class=\"edge\">\n",
+ "<title>7->8</title>\n",
+ "<path fill=\"none\" stroke=\"green\" d=\"M205.3,-214.27C201.23,-188.52 196.25,-157.05 191.97,-129.99\"/>\n",
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+ "</g>\n",
+ "<!-- 8->7 -->\n",
+ "<g id=\"edge19\" class=\"edge\">\n",
+ "<title>8->7</title>\n",
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+ "</g>\n",
+ "<!-- 8->8 -->\n",
+ "<g id=\"edge9\" class=\"edge\">\n",
+ "<title>8->8</title>\n",
+ "<path fill=\"none\" stroke=\"green\" d=\"M231.62,-86.09C243.68,-84.75 252.65,-78.72 252.65,-68 252.65,-60.46 248.21,-55.25 241.39,-52.35\"/>\n",
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+ "<text text-anchor=\"middle\" x=\"256.65\" y=\"-64.9\" font-family=\"Times,serif\" font-size=\"12.00\">0</text>\n",
+ "</g>\n",
+ "<!-- 9 -->\n",
+ "<g id=\"node10\" class=\"node\">\n",
+ "<title>9</title>\n",
+ "</g>\n",
+ "<!-- 9->0 -->\n",
+ "<g id=\"edge10\" class=\"edge\">\n",
+ "<title>9->0</title>\n",
+ "<path fill=\"none\" stroke=\"black\" d=\"M201.32,-804.87C201.32,-790.03 201.32,-767.58 201.32,-745.79\"/>\n",
+ "<polygon fill=\"black\" stroke=\"black\" points=\"204.82,-745.52 201.32,-735.52 197.82,-745.52 204.82,-745.52\"/>\n",
+ "</g>\n",
+ "</g>\n",
+ "</svg>"
],
"text/plain": [
- "<Animation function visualisation>"
+ "<Dot visualization: custom_graph []>"
]
},
- "execution_count": 20,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- ":show"
+ ":dot custom_graph"
]
},
{
@@ -1456,7 +1743,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -1465,7 +1752,7 @@
"Loaded machine: DFA"
]
},
- "execution_count": 21,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -1501,7 +1788,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -1510,7 +1797,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 22,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -1527,8 +1814,10 @@
},
{
"cell_type": "code",
- "execution_count": 23,
- "metadata": {},
+ "execution_count": 21,
+ "metadata": {
+ "scrolled": false
+ },
"outputs": [
{
"data": {
@@ -1634,7 +1923,7 @@
"<Dot visualization: custom_graph []>"
]
},
- "execution_count": 23,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -1642,6 +1931,13 @@
"source": [
":dot custom_graph"
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
diff --git a/info4/kapitel-2/img/konkatenation_M1.svg b/info4/kapitel-2/img/konkatenation_M1.svg
new file mode 100644
index 0000000..e094498
--- /dev/null
+++ b/info4/kapitel-2/img/konkatenation_M1.svg
@@ -0,0 +1 @@
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diff --git a/info4/kapitel-2/img/konkatenation_M2.svg b/info4/kapitel-2/img/konkatenation_M2.svg
new file mode 100644
index 0000000..9831207
--- /dev/null
+++ b/info4/kapitel-2/img/konkatenation_M2.svg
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--
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