diff --git a/info4/kapitel-2/Minimalautomat.ipynb b/info4/kapitel-2/Minimalautomat.ipynb
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+++ b/info4/kapitel-2/Minimalautomat.ipynb
@@ -0,0 +1,1436 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Algorithmus Minimalautomat\n",
+ "\n",
+ "\n",
+ "Hier ist der Beispiel DFA aus den Folien zur Illustration der Konstruktion des Minimalautomaten.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: DFA"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE DFA\n",
+ "SETS\n",
+ " Z = {z0,z1,z2,z3,z4}\n",
+ "ABSTRACT_CONSTANTS δs, L\n",
+ "CONSTANTS Σ, F, δ\n",
+ "PROPERTIES\n",
+ " F ⊆ Z ∧ δ ∈ (Z×Σ) → Z ∧\n",
+ "\n",
+ " /* Definition der erweiterten Überführungsfunktion */\n",
+ " δs ∈ (Z×seq(Σ)) → Z ∧\n",
+ " δs = λ(z,s).(z∈Z ∧ s∈seq(Σ) | \n",
+ " IF s=[] THEN z\n",
+ " ELSE δs(δ(z,first(s)),tail(s)) END)\n",
+ " ∧\n",
+ " /* Die vom Automaten akzeptierte Sprache L */\n",
+ " L = {ω|ω∈seq(Σ) ∧ δs(z0,ω) ∈ F}\n",
+ " ∧\n",
+ " /* Der Automat von Folie 10: */\n",
+ " Σ = {0,1} ∧\n",
+ " F = {z2} ∧\n",
+ " δ = { (z0,0)↦z1, (z0,1)↦z2,\n",
+ " (z1,0)↦z3, (z1,1)↦z3,\n",
+ " (z2,0)↦z4, (z2,1)↦z4,\n",
+ " (z3,0)↦z3, (z3,1)↦z3,\n",
+ " (z4,0)↦z4, (z4,1)↦z4 }\n",
+ "DEFINITIONS\n",
+ " SET_PREF_DOT_HORIZONTAL_LAYOUT==TRUE;\n",
+ " SET_PREF_DOT_LIMIT_PAGE_SIZE==FALSE;\n",
+ " CUSTOM_GRAPH_NODES1 == rec(shape:\"doublecircle\",nodes:F);\n",
+ " CUSTOM_GRAPH_NODES2 == rec(shape:\"circle\",nodes:Z\\F);\n",
+ " CUSTOM_GRAPH_NODES3 == rec(shape:\"none\",color:\"white\",style:\"none\",nodes:{\"\"});\n",
+ " CUSTOM_GRAPH_EDGES1 == rec(color:\"red\",label:\"0\",edges:{a,b|(a,0)|->b:δ});\n",
+ " CUSTOM_GRAPH_EDGES2 == rec(color:\"green\",label:\"1\",edges:{a,b|(a,1)|->b:δ});\n",
+ " CUSTOM_GRAPH_EDGES3 == rec(color:\"black\",label:\"\",edges:{\"\" |-> z0})\n",
+ "END"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine constants set up using operation 0: $setup_constants()"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":constants"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Der Automat sieht grafisch so aus:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
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+ }
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+ "source": [
+ ":dot custom_graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In der folgenden B Maschine sind (bis auf die Entfernung der nicht erreichbaren Zustände) die Schritte des Algorithmus umgesetzt worden.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: MinimalDFA"
+ ]
+ },
+ "execution_count": 62,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE MinimalDFA\n",
+ "SETS\n",
+ " Z = {z0,z1,z2,z3,z4}\n",
+ "ABSTRACT_CONSTANTS δs, L\n",
+ "CONSTANTS Σ, F, δ\n",
+ "PROPERTIES\n",
+ " F ⊆ Z ∧ δ ∈ (Z×Σ) → Z ∧\n",
+ "\n",
+ " /* Definition der erweiterten Überführungsfunktion */\n",
+ " δs ∈ (Z×seq(Σ)) → Z ∧\n",
+ " δs = λ(z,s).(z∈Z ∧ s∈seq(Σ) |\n",
+ " IF s=[] THEN z\n",
+ " ELSE δs(δ(z,first(s)),tail(s)) END)\n",
+ " ∧\n",
+ " /* Die vom Automaten akzeptierte Sprache L */\n",
+ " L = {ω|ω∈seq(Σ) ∧ δs(z0,ω) ∈ F}\n",
+ " ∧\n",
+ " /* Der Automat von Folie 10: */\n",
+ " Σ = {0,1} ∧\n",
+ " F = {z2} ∧\n",
+ " δ = { (z0,0)↦z1, (z0,1)↦z2,\n",
+ " (z1,0)↦z3, (z1,1)↦z3,\n",
+ " (z2,0)↦z4, (z2,1)↦z4,\n",
+ " (z3,0)↦z3, (z3,1)↦z3,\n",
+ " (z4,0)↦z4, (z4,1)↦z4 }\n",
+ "VARIABLES\n",
+ " markiert, fusioniert\n",
+ "INVARIANT markiert : Z <-> Z &\n",
+ " fusioniert : Z <-> Z\n",
+ "INITIALISATION markiert := {za,zb| za∈F ⇔ zb∉F} || fusioniert := {}\n",
+ "OPERATIONS\n",
+ " Markiere(za,zb,a) = SELECT (za,zb) ∉ markiert ∧\n",
+ " a∈Σ ∧\n",
+ " (δ(za,a),δ(zb,a)) ∈ markiert THEN\n",
+ " markiert := markiert \\/ {(za,zb),(zb,za)}\n",
+ " END;\n",
+ " Fertig = SELECT !(za,zb,a).((za,zb) ∉ markiert ∧ a∈Σ\n",
+ " =>\n",
+ " (δ(za,a),δ(zb,a)) ∉ markiert) THEN\n",
+ " fusioniert := {za,zb|(za,zb) ∉ markiert ∧ za ≠ zb} ||\n",
+ " markiert := {}\n",
+ " END\n",
+ "DEFINITIONS\n",
+ " SET_PREF_DOT_HORIZONTAL_LAYOUT==TRUE;\n",
+ " SET_PREF_DOT_LIMIT_PAGE_SIZE==FALSE;\n",
+ " CUSTOM_GRAPH_NODES1 == rec(shape:\"doublecircle\",nodes:F);\n",
+ " CUSTOM_GRAPH_NODES2 == rec(shape:\"circle\",nodes:Z\\F);\n",
+ " CUSTOM_GRAPH_NODES3 == rec(shape:\"none\",color:\"white\",style:\"none\",nodes:{\"\"});\n",
+ " CUSTOM_GRAPH_EDGES1 == rec(color:\"red\",label:\"0\",edges:{a,b|(a,0)|->b∈δ});\n",
+ " CUSTOM_GRAPH_EDGES2 == rec(color:\"green\",label:\"1\",edges:{a,b|(a,1)|->b∈δ});\n",
+ " CUSTOM_GRAPH_EDGES3 == rec(color:\"black\",label:\"\",edges:{\"\" |-> z0});\n",
+ " CUSTOM_GRAPH_EDGES4 == rec(color:\"gray\",label:\"×\",style:\"dotted\",edges:markiert);\n",
+ " CUSTOM_GRAPH_EDGES5 == rec(color:\"purple\",label:\"↔\",style:\"bold\",edges:fusioniert)\n",
+ "END"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine constants set up using operation 0: $setup_constants()"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":constants"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine initialised using operation 1: $initialise_machine()"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Markiere alle Paare $\\{z, z'\\}$ mit \n",
+ "\n",
+ "* $z \\in F \\Longleftrightarrow z' \\not\\in F$.\n",
+ "\n",
+ "Dies wird in der B Maschine in der INITIALISATION Klausel gemacht. Im Graphen unten sind die markierten Paare mit $\\times$ gekennzeichnet."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Preference changed: DOT_ENGINE = circo\n"
+ ]
+ },
+ "execution_count": 66,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":pref DOT_ENGINE=circo"
+ ]
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+ "metadata": {},
+ "outputs": [
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+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Sei $\\{z, z'\\}$ ein unmarkiertes Paar. Prüfe für jedes\n",
+ " $a \\in \\Sigma$, ob $\\{\\delta(z,a), \\delta(z',a)\\}$ bereits markiert\n",
+ " ist. Ist mindestens ein Test erfolgreich, so markiere auch\n",
+ " $\\{z,z'\\}$.\n",
+ " \n",
+ " Dies ist hier der Fall:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: Markiere(z1,z0,1)"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec Markiere"
+ ]
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+ "<g id=\"edge24\" class=\"edge\"><title>2->4</title>\n",
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+ "<g id=\"edge26\" class=\"edge\"><title>3->2</title>\n",
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+ "<g id=\"edge30\" class=\"edge\"><title>4->2</title>\n",
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+ "<!-- 4->3 -->\n",
+ "<g id=\"edge32\" class=\"edge\"><title>4->3</title>\n",
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+ "<!-- 5->1 -->\n",
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+ ],
+ "text/plain": [
+ "<Dot visualization: custom_graph []>"
+ ]
+ },
+ "execution_count": 75,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":dot custom_graph"
+ ]
+ },
+ {
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+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
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+}