diff --git a/info4/kapitel-5/TuringMaschine.ipynb b/info4/kapitel-5/TuringMaschine.ipynb
index b70358a1f9f228301f56fadc8e2133801fe75fd4..bbe7e86371211474cd32a436711bef0d15d2b956 100644
--- a/info4/kapitel-5/TuringMaschine.ipynb
+++ b/info4/kapitel-5/TuringMaschine.ipynb
@@ -47,34 +47,34 @@
" δ : (States * Alphabet) <-> (States * Alphabet * Direction) &\n",
"\n",
" δ = { /* Neuer Zyklus */\n",
- " (z0,a) |-> (z1,X,R),\n",
- " (z0,X) |-> (z0,X,R),\n",
+ " (z0,a) ↦ (z1,X,R),\n",
+ " (z0,X) ↦ (z0,X,R),\n",
" \n",
" /* ein a getilgt (X), nächstes b suchen */\n",
- " (z1,a) |-> (z1,a,R),\n",
- " (z1,b) |-> (z2,X,R),\n",
- " (z1,X) |-> (z1,X,R),\n",
+ " (z1,a) ↦ (z1,a,R),\n",
+ " (z1,b) ↦ (z2,X,R),\n",
+ " (z1,X) ↦ (z1,X,R),\n",
" \n",
" /* ein a,b getilgt (X), nächstes c suchen */\n",
- " (z2,b) |-> (z2,b,R),\n",
- " (z2,c) |-> (z3,X,R),\n",
- " (z2,X) |-> (z2,X,R),\n",
+ " (z2,b) ↦ (z2,b,R),\n",
+ " (z2,c) ↦ (z3,X,R),\n",
+ " (z2,X) ↦ (z2,X,R),\n",
" \n",
" /* ein a,b,c getilgt (X), rechten Rand suchen */\n",
- " (z3,c) |-> (z3,c,R),\n",
- " (z3,Blank) |-> (z4,Blank,L),\n",
+ " (z3,c) ↦ (z3,c,R),\n",
+ " (z3,Blank) ↦ (z4,Blank,L),\n",
" \n",
" /* Zurücklaufen und testen ob alle a,b,c getilgt */\n",
- " (z4,X) |-> (z4,X,L),\n",
- " (z4,Blank) |-> (z6,Blank,R), /* Erfolg ! */\n",
- " (z4,c) |-> (z5,c,L), \n",
+ " (z4,X) ↦ (z4,X,L),\n",
+ " (z4,Blank) ↦ (z6,Blank,R), /* Erfolg ! */\n",
+ " (z4,c) ↦ (z5,c,L), \n",
" \n",
" /* Test nicht erfolgreich; zum linken Rand zurücklaufen und neuer Zyklus */\n",
- " (z5,X) |-> (z5,X,L),\n",
- " (z5,Blank) |-> (z0,Blank,R),\n",
- " (z5,a) |-> (z5,a,L),\n",
- " (z5,b) |-> (z5,b,L),\n",
- " (z5,c) |-> (z5,c,L)\n",
+ " (z5,X) ↦ (z5,X,L),\n",
+ " (z5,Blank) ↦ (z0,Blank,R),\n",
+ " (z5,a) ↦ (z5,a,L),\n",
+ " (z5,b) ↦ (z5,b,L),\n",
+ " (z5,c) ↦ (z5,c,L)\n",
" } &\n",
" Final = {z6}\n",
"VARIABLES Left,cur,Right\n",
@@ -86,9 +86,9 @@
" Accept = PRE cur : Final THEN skip END;\n",
" GoTo(z,S,znew,NewSymbol,Dir) =\n",
" PRE z=cur & S=CurSymbol &\n",
- " (z, S) |-> (znew,NewSymbol,Dir) : δ THEN\n",
+ " (z, S) ↦ (znew,NewSymbol,Dir) : δ THEN\n",
" ANY tail_Right \n",
- " WHERE (Right=[] => tail_Right=[]) & (Right/=[] => tail_Right = tail(Right)) THEN\n",
+ " WHERE (Right=[] ⇒ tail_Right=[]) & (Right/=[] ⇒ tail_Right = tail(Right)) THEN\n",
" cur := znew ||\n",
" IF Dir = N THEN\n",
" Right := NewSymbol -> tail_Right\n",
diff --git a/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb b/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..7584e7525c6ba9af4dc5847be48a331bdef8d159
--- /dev/null
+++ b/info4/kapitel-7/TuringMaschineBerechenbarkeit.ipynb
@@ -0,0 +1,1389 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Turing Maschinen und Berechenbarkeit\n",
+ "\n",
+ "Bisher wurden Turingmaschinen als Akzeptoren definiert. \n",
+ "\n",
+ "Nun wollen wir Turingmaschinen als Maschinen zur Berechnung von\n",
+ "Funktionen auffassen.\n",
+ "\n",
+ "\n",
+ " Eine Funktion $f: \\nats^k \\rightarrow \\nats$ heißt \n",
+ " __Turing-berechenbar__, falls es eine deterministische\n",
+ " Turingmaschine $M=(\\Sigma, \\Gamma, Z, \\delta ,z_0, \\Box, F)$ \n",
+ " mit $\\Sigma = \\{0,1\\}$ \n",
+ " gibt,\n",
+ " so dass für alle $n_1, n_2, \\ldots , n_k, m \\in \\nats$:\n",
+ " \n",
+ "* $f(n_1, n_2, \\ldots , n_k) = m$ $\\Leftrightarrow$\n",
+ "* $\\exists z\\in F . z_0 \\mbox{bin}(n_1) \\#\n",
+ "\\mbox{bin}(n_2) \\# \\cdots \\# \\mbox{bin}(n_k) \\vdash_{M}^{\\ast} z\n",
+ "\\mbox{bin}(m)$\n",
+ "\n",
+ "Falls $f(n_1, n_2, \\ldots , n_k)$ nicht definiert ist, läuft $M$ in\n",
+ "eine unendliche Schleife oder stoppt in einem Zustand $z\\not\\in F$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " Die (total definierte) \\alert{\\em Nachfolgerfunktion} $f: \\nats \\rightarrow \\nats$ mit\n",
+ "* $f:n\\rightarrow n+1$\n",
+ "ist Turing-berechenbar."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: TuringMachine_2"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE TuringMachine_2\n",
+ "/* B Modell einer 1-band Turing Maschine */\n",
+ "/* by Michael Leuschel, 2012 */\n",
+ "/* The turing machine implements the +1 function on binary numbers */\n",
+ "/* See Slide 2 from folien-kapitel-7.pdf (Info 4) */\n",
+ "SETS\n",
+ " Alphabet ={O,I,Blank};\n",
+ " Z = {z0,z1,z2,ze};\n",
+ " Direction = {L,R,N}\n",
+ "DEFINITIONS\n",
+ " Σ == {O,I};\n",
+ " Γ == Σ;\n",
+ " CurSymbol == (Right<-Blank)(1);\n",
+ " ANIMATION_FUNCTION_DEFAULT == {(1,0,cur)};\n",
+ " ANIMATION_FUNCTION1 == {1} *( (%i.(i∈-size(Left)..-1|i+size(Left)+1) ; Left) \\/ Right)\n",
+ "CONSTANTS Final, δ\n",
+ "PROPERTIES\n",
+ " Final ⊆ Z ∧\n",
+ " δ ∈ (Z * Alphabet) <-> (Z * Alphabet * Direction) ∧\n",
+ "\n",
+ " δ = { (z0,O) ↦ (z0,O,R), (z0,I) ↦ (z0,I,R), (z0,Blank) ↦ (z1,Blank,L),\n",
+ " (z1,O) ↦ (z2,I,L), (z1,I) ↦ (z1,O,L), (z1,Blank) ↦ (ze,I,N),\n",
+ " (z2,O) ↦ (z2,O,L), (z2,I) ↦ (z2,I,L), (z2,Blank) ↦ (ze,Blank,R)\n",
+ " } ∧\n",
+ " Final = {ze}\n",
+ "VARIABLES Left,cur,Right\n",
+ "INVARIANT\n",
+ " cur ∈ Z ∧\n",
+ " Left ∈ seq(Alphabet) ∧ Right ∈ seq(Alphabet)\n",
+ "INITIALISATION Left,cur,Right := [],z0,[I,I,I,I,I] // [I,O,I]\n",
+ "OPERATIONS\n",
+ " Accept = PRE cur : Final THEN\n",
+ " Left,cur,Right := [],z0,Right /* restart machine with previous number */\n",
+ " END;\n",
+ " GoTo(z,S,znew,NewSymbol,Dir) =\n",
+ " PRE z=cur ∧ S=CurSymbol ∧\n",
+ " (z, S) ↦ (znew,NewSymbol,Dir) ∈ δ THEN\n",
+ " ANY tail_Right \n",
+ " WHERE (Right=[] ⇒ tail_Right=[]) ∧\n",
+ " (Right/=[] ⇒ tail_Right = tail(Right)) THEN\n",
+ " cur := znew ||\n",
+ " IF Dir = N THEN\n",
+ " Right := NewSymbol -> tail_Right\n",
+ " ELSIF Dir = R THEN\n",
+ " Left,Right := Left <- NewSymbol, tail_Right\n",
+ " ELSIF Left=[] THEN\n",
+ " Left,Right := [], Blank -> (NewSymbol -> tail_Right)\n",
+ " ELSE\n",
+ " Left,Right := front(Left), last(Left) -> (NewSymbol -> tail_Right)\n",
+ " END\n",
+ " END\n",
+ " END\n",
+ "END\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine constants set up using operation 0: $setup_constants()"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":constants"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine initialised using operation 1: $initialise_machine()"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Turing Maschine wird mit der Binärzahl 11111 (31 als Dezimalzahl) aufgerufen."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 23,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,Blank,z1,Blank,L)"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,I,z1,O,L)"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,I,z1,O,L)"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 34,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,I,z1,O,L)"
+ ]
+ },
+ "execution_count": 35,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,I,z1,O,L)"
+ ]
+ },
+ "execution_count": 37,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 38,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,I,z1,O,L)"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,Blank,ze,I,N)"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">ze</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: Accept()"
+ ]
+ },
+ "execution_count": 44,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec Accept"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Turing Maschine hat 32 als Ergebnis ausgerechnet. Wir können die Maschine wieder mit 32 als Eingabe starten:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,I,z0,I,R)"
+ ]
+ },
+ "execution_count": 47,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,O,z0,O,R)"
+ ]
+ },
+ "execution_count": 49,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">z0</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,O,z0,O,R)"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,O,z0,O,R)"
+ ]
+ },
+ "execution_count": 52,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,O,z0,O,R)"
+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,O,z0,O,R)"
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z0,Blank,z1,Blank,L)"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">z1</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z1,O,z2,I,L)"
+ ]
+ },
+ "execution_count": 58,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">z2</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,O,z2,O,L)"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,O,z2,O,L)"
+ ]
+ },
+ "execution_count": 61,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,O,z2,O,L)"
+ ]
+ },
+ "execution_count": 62,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,O,z2,O,L)"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,I,z2,I,L)"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">z2</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 65,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: GoTo(z2,Blank,ze,Blank,R)"
+ ]
+ },
+ "execution_count": 66,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec GoTo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "<td style=\"padding:10px\">ze</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">O</td>\n",
+ "<td style=\"padding:10px\">I</td>\n",
+ "<td style=\"padding:10px\">Blank</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 67,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Turing Maschine at 33 als Ergebnis zurückgegeben."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Executed operation: Accept()"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":exec Accept"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "ProB 2",
+ "language": "prob",
+ "name": "prob2"
+ },
+ "language_info": {
+ "codemirror_mode": "prob2_jupyter_repl",
+ "file_extension": ".prob",
+ "mimetype": "text/x-prob2-jupyter-repl",
+ "name": "prob"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}