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prob-teaching-notebooks
Commits
15c2a0e6
Commit
15c2a0e6
authored
5 years ago
by
Michael Leuschel
Browse files
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fix PP_SEQUENCES preference
parent
3bd07894
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1 changed file
info4/kapitel-3/PDA-Kellerautomaten.ipynb
+145
-145
145 additions, 145 deletions
info4/kapitel-3/PDA-Kellerautomaten.ipynb
with
145 additions
and
145 deletions
info4/kapitel-3/PDA-Kellerautomaten.ipynb
+
145
−
145
View file @
15c2a0e6
...
...
@@ -31,7 +31,7 @@
},
{
"cell_type": "code",
"execution_count":
44
,
"execution_count":
59
,
"metadata": {},
"outputs": [
{
...
...
@@ -40,7 +40,7 @@
"Loaded machine: PDA"
]
},
"execution_count":
44
,
"execution_count":
59
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -60,7 +60,7 @@
" ANIMATION_FUNCTION == {2}*α ∪ {3}*(γ);\n",
" ANIMATION_FUNCTION1 == {(1,0,\"z: \"),(2,0,\"α:\"),(3,0,\"γ:\")};\n",
" ANIMATION_STR_JUSTIFY_LEFTx == TRUE;\n",
" SET_PREF_P
RETTY_PRINT
_SEQUENCES == TRUE\n",
" SET_PREF_P
P
_SEQUENCES == TRUE\n",
"CONSTANTS δ\n",
"PROPERTIES\n",
" /* Der PDA für {a^m b^m| m>=1} ; Beispiel von Info 4 (Folie 95ff) */\n",
...
...
@@ -104,7 +104,7 @@
},
{
"cell_type": "code",
"execution_count":
45
,
"execution_count":
60
,
"metadata": {},
"outputs": [
{
...
...
@@ -113,7 +113,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
"execution_count":
45
,
"execution_count":
60
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -124,7 +124,7 @@
},
{
"cell_type": "code",
"execution_count":
4
6,
"execution_count": 6
1
,
"metadata": {},
"outputs": [
{
...
...
@@ -133,7 +133,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
"execution_count":
4
6,
"execution_count": 6
1
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -144,7 +144,7 @@
},
{
"cell_type": "code",
"execution_count":
47
,
"execution_count":
62
,
"metadata": {},
"outputs": [
{
...
...
@@ -178,7 +178,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
47
,
"execution_count":
62
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -189,7 +189,7 @@
},
{
"cell_type": "code",
"execution_count":
48
,
"execution_count":
63
,
"metadata": {},
"outputs": [
{
...
...
@@ -200,10 +200,10 @@
"Constants: δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z0,
{(1|->A),(2|->
BOT
)}
)"
"Schritt(z0,
[A,
BOT
]
)"
]
},
"execution_count":
48
,
"execution_count":
63
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -214,16 +214,16 @@
},
{
"cell_type": "code",
"execution_count": 4
9
,
"execution_count":
6
4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{(1|->A),(2|->
BOT
)}
)"
"Executed operation: Schritt(z0,
[A,
BOT
]
)"
]
},
"execution_count": 4
9
,
"execution_count":
6
4,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -234,7 +234,7 @@
},
{
"cell_type": "code",
"execution_count": 5
0
,
"execution_count":
6
5,
"metadata": {},
"outputs": [
{
...
...
@@ -265,7 +265,7 @@
"<Animation function visualisation>"
]
},
"execution_count": 5
0
,
"execution_count":
6
5,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -276,19 +276,19 @@
},
{
"cell_type": "code",
"execution_count":
51
,
"execution_count":
66
,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
"$(\\mathit{z0}\\mapsto
\\{(1\\mapsto \\mathit{a}),(2\\mapsto \\mathit{b}),(3\\mapsto \\mathit{b})\\}\\mapsto\\{(1\\mapsto \\mathit{A}),(2\\mapsto \\mathit{BOT})\\}
)$"
"$(\\mathit{z0}\\mapsto
[a,\\mathit{b},b]\\mapsto [A,BOT]
)$"
],
"text/plain": [
"(z0↦
{(1↦a),(2↦b),(3↦b)}↦{(1↦A),(2↦
BOT
)}
)"
"(z0↦
[a,b,b]↦[A,
BOT
]
)"
]
},
"execution_count":
51
,
"execution_count":
66
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -299,7 +299,7 @@
},
{
"cell_type": "code",
"execution_count":
52
,
"execution_count":
67
,
"metadata": {},
"outputs": [
{
...
...
@@ -310,10 +310,10 @@
"Constants: δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z0,
{(1|->A),(2|->A)}
)"
"Schritt(z0,
[A,A]
)"
]
},
"execution_count":
52
,
"execution_count":
67
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -324,16 +324,16 @@
},
{
"cell_type": "code",
"execution_count":
53
,
"execution_count":
68
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{(1|->A),(2|->A)}
)"
"Executed operation: Schritt(z0,
[A,A]
)"
]
},
"execution_count":
53
,
"execution_count":
68
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -344,7 +344,7 @@
},
{
"cell_type": "code",
"execution_count":
54
,
"execution_count":
69
,
"metadata": {},
"outputs": [
{
...
...
@@ -375,7 +375,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
54
,
"execution_count":
69
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -386,7 +386,7 @@
},
{
"cell_type": "code",
"execution_count":
55
,
"execution_count":
70
,
"metadata": {},
"outputs": [
{
...
...
@@ -397,10 +397,10 @@
"Constants: δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z1,
{}
)"
"Schritt(z1,
[]
)"
]
},
"execution_count":
55
,
"execution_count":
70
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -411,16 +411,16 @@
},
{
"cell_type": "code",
"execution_count":
56
,
"execution_count":
71
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z1,
{}
)"
"Executed operation: Schritt(z1,
[]
)"
]
},
"execution_count":
56
,
"execution_count":
71
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -431,7 +431,7 @@
},
{
"cell_type": "code",
"execution_count":
5
7,
"execution_count": 7
2
,
"metadata": {},
"outputs": [
{
...
...
@@ -459,7 +459,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
5
7,
"execution_count": 7
2
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -470,7 +470,7 @@
},
{
"cell_type": "code",
"execution_count":
58
,
"execution_count":
73
,
"metadata": {},
"outputs": [
{
...
...
@@ -481,10 +481,10 @@
"Constants: δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z1,
{}
)"
"Schritt(z1,
[]
)"
]
},
"execution_count":
58
,
"execution_count":
73
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -495,16 +495,16 @@
},
{
"cell_type": "code",
"execution_count":
59
,
"execution_count":
74
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z1,
{}
)"
"Executed operation: Schritt(z1,
[]
)"
]
},
"execution_count":
59
,
"execution_count":
74
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -515,7 +515,7 @@
},
{
"cell_type": "code",
"execution_count":
60
,
"execution_count":
75
,
"metadata": {},
"outputs": [
{
...
...
@@ -540,7 +540,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
60
,
"execution_count":
75
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -551,7 +551,7 @@
},
{
"cell_type": "code",
"execution_count": 6
1
,
"execution_count":
7
6,
"metadata": {},
"outputs": [
{
...
...
@@ -562,10 +562,10 @@
"Constants: δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"LambdaSchritt(z1,
{}
)"
"LambdaSchritt(z1,
[]
)"
]
},
"execution_count": 6
1
,
"execution_count":
7
6,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -576,16 +576,16 @@
},
{
"cell_type": "code",
"execution_count":
62
,
"execution_count":
77
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: LambdaSchritt(z1,
{}
)"
"Executed operation: LambdaSchritt(z1,
[]
)"
]
},
"execution_count":
62
,
"execution_count":
77
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -596,7 +596,7 @@
},
{
"cell_type": "code",
"execution_count":
63
,
"execution_count":
78
,
"metadata": {},
"outputs": [
{
...
...
@@ -621,7 +621,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
63
,
"execution_count":
78
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -632,7 +632,7 @@
},
{
"cell_type": "code",
"execution_count":
64
,
"execution_count":
79
,
"metadata": {},
"outputs": [
{
...
...
@@ -646,7 +646,7 @@
"Akzeptieren()"
]
},
"execution_count":
64
,
"execution_count":
79
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -657,7 +657,7 @@
},
{
"cell_type": "code",
"execution_count":
65
,
"execution_count":
80
,
"metadata": {},
"outputs": [
{
...
...
@@ -666,7 +666,7 @@
"Executed operation: Akzeptieren()"
]
},
"execution_count":
65
,
"execution_count":
80
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -693,23 +693,23 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 3
4
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Loaded machine: PDA"
"Loaded machine: PDA
_für_kfG
"
]
},
"execution_count": 3,
"execution_count": 3
4
,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"::load\n",
"MACHINE PDA\n",
"MACHINE PDA
_für_kfG
\n",
"/* B Modell eines PDA */\n",
"SETS\n",
" Z = {z0}; // die Zustände des Automaten, z0 ist der Startzustand\n",
...
...
@@ -723,7 +723,7 @@
" ANIMATION_FUNCTION == {2}*α ∪ {3}*(γ);\n",
" ANIMATION_FUNCTION1 == {(1,0,\"z: \"),(2,0,\"α:\"),(3,0,\"γ:\")};\n",
" ANIMATION_STR_JUSTIFY_LEFTx == TRUE;\n",
" SET_PREF_P
RETTY_PRINT
_SEQUENCES == TRUE\n",
" SET_PREF_P
P
_SEQUENCES == TRUE\n",
"CONSTANTS P, δ\n",
"PROPERTIES\n",
"/* Die Grammatik Regeln */\n",
...
...
@@ -773,7 +773,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count":
3
5,
"metadata": {},
"outputs": [
{
...
...
@@ -782,7 +782,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
"execution_count": 5,
"execution_count":
3
5,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -793,7 +793,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count":
3
6,
"metadata": {},
"outputs": [
{
...
...
@@ -802,7 +802,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
"execution_count": 6,
"execution_count":
3
6,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -813,7 +813,7 @@
},
{
"cell_type": "code",
"execution_count": 3
3
,
"execution_count": 3
7
,
"metadata": {},
"outputs": [
{
...
...
@@ -821,28 +821,28 @@
"text/markdown": [
"|z|x|X|z2|Xs|\n",
"|---|---|---|---|---|\n",
"|$\\
renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\renewcommand{\\emptyset}{\\mathord\\varnothing}\\
mathit{z0}$|$\\mathit{a}$|$\\mathit{a}$|$\\mathit{z0}$|$
\\emptyset
$|\n",
"|$\\mathit{z0}$|$\\mathit{b}$|$\\mathit{b}$|$\\mathit{z0}$|$
\\emptyset
$|\n",
"|$\\mathit{z0}$|$\\mathit{S}$|$\\mathit{S}$|$\\mathit{z0}$|$
\\emptyset
$|\n",
"|$\\mathit{z0}$|$\\mathit{C}$|$\\mathit{C}$|$\\mathit{z0}$|$
\\emptyset
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{S}$|$\\mathit{z0}$|$
\\{(1\\mapsto \\mathit{C})\\}
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{S}$|$\\mathit{z0}$|$
\\{(1\\mapsto \\mathit{a}),(2\\mapsto \\mathit{S}),(3\\mapsto \\mathit{b})\\}
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{C}$|$\\mathit{z0}$|$
\\{(1\\mapsto \\mathit{a}),(2\\mapsto \\mathit{b})\\}
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{lambda}$|$\\mathit{z0}$|$
\\emptyset
$|\n"
"|$\\mathit{z0}$|$\\mathit{a}$|$\\mathit{a}$|$\\mathit{z0}$|$
[]
$|\n",
"|$\\mathit{z0}$|$\\mathit{b}$|$\\mathit{b}$|$\\mathit{z0}$|$
[]
$|\n",
"|$\\mathit{z0}$|$\\mathit{S}$|$\\mathit{S}$|$\\mathit{z0}$|$
[]
$|\n",
"|$\\mathit{z0}$|$\\mathit{C}$|$\\mathit{C}$|$\\mathit{z0}$|$
[]
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{S}$|$\\mathit{z0}$|$
[C]
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{S}$|$\\mathit{z0}$|$
[a,\\mathit{S},b]
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{C}$|$\\mathit{z0}$|$
[a,b]
$|\n",
"|$\\mathit{z0}$|$\\mathit{lambda}$|$\\mathit{lambda}$|$\\mathit{z0}$|$
[]
$|\n"
],
"text/plain": [
"z\tx\tX\tz2\tXs\n",
"z0\ta\ta\tz0\t
{}
\n",
"z0\tb\tb\tz0\t
{}
\n",
"z0\tS\tS\tz0\t
{}
\n",
"z0\tC\tC\tz0\t
{}
\n",
"z0\tlambda\tS\tz0\t
{(1|->C)}
\n",
"z0\tlambda\tS\tz0\t
{(1|->a),(2|->S),(3|->b)}
\n",
"z0\tlambda\tC\tz0\t
{(1|->a),(2|->b)}
\n",
"z0\tlambda\tlambda\tz0\t
{}
\n"
"z0\ta\ta\tz0\t
[]
\n",
"z0\tb\tb\tz0\t
[]
\n",
"z0\tS\tS\tz0\t
[]
\n",
"z0\tC\tC\tz0\t
[]
\n",
"z0\tlambda\tS\tz0\t
[C]
\n",
"z0\tlambda\tS\tz0\t
[a,S,b]
\n",
"z0\tlambda\tC\tz0\t
[a,b]
\n",
"z0\tlambda\tlambda\tz0\t
[]
\n"
]
},
"execution_count": 3
3
,
"execution_count": 3
7
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -853,7 +853,7 @@
},
{
"cell_type": "code",
"execution_count":
7
,
"execution_count":
38
,
"metadata": {},
"outputs": [
{
...
...
@@ -887,7 +887,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
7
,
"execution_count":
38
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -898,22 +898,22 @@
},
{
"cell_type": "code",
"execution_count":
8
,
"execution_count":
39
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Machine: PDA\n",
"Machine: PDA
_für_kfG
\n",
"Sets: Z, SYMBOLE\n",
"Constants: P, δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"LambdaSchritt(z0,
{(1|->C)}
)\n",
"LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)"
"LambdaSchritt(z0,
[C]
)\n",
"LambdaSchritt(z0,
[a,S,b]
)"
]
},
"execution_count":
8
,
"execution_count":
39
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -924,16 +924,16 @@
},
{
"cell_type": "code",
"execution_count":
9
,
"execution_count":
40
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)"
"Executed operation: LambdaSchritt(z0,
[a,S,b]
)"
]
},
"execution_count":
9
,
"execution_count":
40
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -944,7 +944,7 @@
},
{
"cell_type": "code",
"execution_count": 1
0
,
"execution_count":
4
1,
"metadata": {},
"outputs": [
{
...
...
@@ -978,7 +978,7 @@
"<Animation function visualisation>"
]
},
"execution_count": 1
0
,
"execution_count":
4
1,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -989,21 +989,21 @@
},
{
"cell_type": "code",
"execution_count":
11
,
"execution_count":
42
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Machine: PDA\n",
"Machine: PDA
_für_kfG
\n",
"Sets: Z, SYMBOLE\n",
"Constants: P, δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z0,
{}
)"
"Schritt(z0,
[]
)"
]
},
"execution_count":
11
,
"execution_count":
42
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1014,16 +1014,16 @@
},
{
"cell_type": "code",
"execution_count":
1
3,
"execution_count":
4
3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{}
)"
"Executed operation: Schritt(z0,
[]
)"
]
},
"execution_count":
1
3,
"execution_count":
4
3,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1034,7 +1034,7 @@
},
{
"cell_type": "code",
"execution_count":
1
4,
"execution_count":
4
4,
"metadata": {},
"outputs": [
{
...
...
@@ -1065,7 +1065,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
1
4,
"execution_count":
4
4,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1076,22 +1076,22 @@
},
{
"cell_type": "code",
"execution_count":
1
5,
"execution_count":
4
5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Machine: PDA\n",
"Machine: PDA
_für_kfG
\n",
"Sets: Z, SYMBOLE\n",
"Constants: P, δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"LambdaSchritt(z0,
{(1|->C)}
)\n",
"LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)"
"LambdaSchritt(z0,
[C]
)\n",
"LambdaSchritt(z0,
[a,S,b]
)"
]
},
"execution_count":
1
5,
"execution_count":
4
5,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1102,16 +1102,16 @@
},
{
"cell_type": "code",
"execution_count":
1
6,
"execution_count":
4
6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: LambdaSchritt(z0,
{(1|->C)}
)"
"Executed operation: LambdaSchritt(z0,
[C]
)"
]
},
"execution_count":
1
6,
"execution_count":
4
6,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1122,7 +1122,7 @@
},
{
"cell_type": "code",
"execution_count":
1
7,
"execution_count":
4
7,
"metadata": {},
"outputs": [
{
...
...
@@ -1153,7 +1153,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
1
7,
"execution_count":
4
7,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1164,21 +1164,21 @@
},
{
"cell_type": "code",
"execution_count":
1
8,
"execution_count":
4
8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Machine: PDA\n",
"Machine: PDA
_für_kfG
\n",
"Sets: Z, SYMBOLE\n",
"Constants: P, δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"LambdaSchritt(z0,
{(1|->a),(2|->b)}
)"
"LambdaSchritt(z0,
[a,b]
)"
]
},
"execution_count":
1
8,
"execution_count":
4
8,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1189,16 +1189,16 @@
},
{
"cell_type": "code",
"execution_count":
1
9,
"execution_count":
4
9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: LambdaSchritt(z0,
{(1|->a),(2|->b)}
)"
"Executed operation: LambdaSchritt(z0,
[a,b]
)"
]
},
"execution_count":
1
9,
"execution_count":
4
9,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1209,7 +1209,7 @@
},
{
"cell_type": "code",
"execution_count":
2
0,
"execution_count":
5
0,
"metadata": {},
"outputs": [
{
...
...
@@ -1240,7 +1240,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
2
0,
"execution_count":
5
0,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1251,21 +1251,21 @@
},
{
"cell_type": "code",
"execution_count":
22
,
"execution_count":
51
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Machine: PDA\n",
"Machine: PDA
_für_kfG
\n",
"Sets: Z, SYMBOLE\n",
"Constants: P, δ\n",
"Variables: z, α, γ\n",
"Operations: \n",
"Schritt(z0,
{}
)"
"Schritt(z0,
[]
)"
]
},
"execution_count":
22
,
"execution_count":
51
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1276,16 +1276,16 @@
},
{
"cell_type": "code",
"execution_count": 2
3
,
"execution_count":
5
2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{}
)"
"Executed operation: Schritt(z0,
[]
)"
]
},
"execution_count": 2
3
,
"execution_count":
5
2,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1296,7 +1296,7 @@
},
{
"cell_type": "code",
"execution_count":
24
,
"execution_count":
53
,
"metadata": {},
"outputs": [
{
...
...
@@ -1324,7 +1324,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
24
,
"execution_count":
53
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1335,16 +1335,16 @@
},
{
"cell_type": "code",
"execution_count":
2
5,
"execution_count": 5
4
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{}
)"
"Executed operation: Schritt(z0,
[]
)"
]
},
"execution_count":
2
5,
"execution_count": 5
4
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1355,7 +1355,7 @@
},
{
"cell_type": "code",
"execution_count":
26
,
"execution_count":
55
,
"metadata": {},
"outputs": [
{
...
...
@@ -1380,7 +1380,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
26
,
"execution_count":
55
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1391,16 +1391,16 @@
},
{
"cell_type": "code",
"execution_count":
27
,
"execution_count":
56
,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: Schritt(z0,
{}
)"
"Executed operation: Schritt(z0,
[]
)"
]
},
"execution_count":
27
,
"execution_count":
56
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1411,7 +1411,7 @@
},
{
"cell_type": "code",
"execution_count":
28
,
"execution_count":
57
,
"metadata": {},
"outputs": [
{
...
...
@@ -1436,7 +1436,7 @@
"<Animation function visualisation>"
]
},
"execution_count":
28
,
"execution_count":
57
,
"metadata": {},
"output_type": "execute_result"
}
...
...
@@ -1447,7 +1447,7 @@
},
{
"cell_type": "code",
"execution_count":
30
,
"execution_count":
58
,
"metadata": {},
"outputs": [
{
...
...
@@ -1456,7 +1456,7 @@
"Executed operation: Akzeptieren()"
]
},
"execution_count":
30
,
"execution_count":
58
,
"metadata": {},
"output_type": "execute_result"
}
...
...
%% Cell type:markdown id: tags:
# PDA (Push Down Automata - Kellerautomaten)
%% Cell type:markdown id: tags:
Ein __(nichtdeterministischer) Kellerautomat__
(kurz PDA für __push-down automaton__) ist ein $6$-Tupel
$M = (
\S
igma,
\G
amma, Z,
\d
elta , z_0,
\#
)$, wobei
*
$
\S
igma$ das Eingabe-Alphabet ist,
*
$
\G
amma$ das Kelleralphabet,
*
$Z$ eine endliche Menge von Zuständen,
*
$
\d
elta : Z
\t
imes (
\S
igma
\c
up
\{\l
ambda
\}
)
\t
imes
\G
amma
\r
ightarrow
\m
athfrak{P}_e(Z
\t
imes
\G
amma^{
\a
st})$ die
Überführungsfunktion,
*
$z_0
\i
n Z$ der Startzustand,
*
$
\#
\i
n
\G
amma$ das Bottom-Symbol im Keller.
Anmerkung: $
\m
athfrak{P}_e(Z
\t
imes
\G
amma^{
\a
st})$ ist die Menge aller
__endlichen__ Teilmengen von $Z
\t
imes
\G
amma^{
\a
st}$.
%% Cell type:code id: tags:
```
prob
::load
MACHINE PDA
/* B Modell eines PDA */
SETS
Z = {z0,z1}; // die Zustände des Automaten, z0 ist der Startzustand
SYMBOLE={a,b, A, BOT, lambda} /* BOT = # = Bottom-Symbol im Keller*/
DEFINITIONS
Σ == {a,b}; // das Eingabe-Alphabet
Γ == {A,BOT}; // das Kelleralphabet
ANIMATION_FUNCTION_DEFAULT == {(1,1,z)};
ANIMATION_FUNCTION == {2}*α ∪ {3}*(γ);
ANIMATION_FUNCTION1 == {(1,0,"z: "),(2,0,"α:"),(3,0,"γ:")};
ANIMATION_STR_JUSTIFY_LEFTx == TRUE;
SET_PREF_P
RETTY_PRINT
_SEQUENCES == TRUE
SET_PREF_P
P
_SEQUENCES == TRUE
CONSTANTS δ
PROPERTIES
/* Der PDA für {a^m b^m| m>=1} ; Beispiel von Info 4 (Folie 95ff) */
δ = { (z0,a,BOT) ↦ (z0,[A,BOT]),
(z0,a,A) ↦ (z0,[A,A]),
(z0,b,A) ↦ (z1,[]),
(z1,lambda,BOT) ↦ (z1,[]),
(z1,b,A) ↦ (z1,[]) }
// Anmerkung: δ ist hier als Relation anstatt als Funktion zu Mengen definiert
// Deshalb entspricht δ[{(z,a,g)}] in der B Maschine δ(z,a,g) aus dem Skript
VARIABLES
z, α, γ // Konfiguration in dem sich der PDA befindet
INVARIANT
z ∈ Z ∧ // der aktuelle Zustand
α ∈ seq(Σ) ∧ // der noch zu lesende Teil des Eingabeworts
γ ∈ seq(Γ) // aktuelle Kellerinhalt
INITIALISATION
z := z0 ||
γ := [BOT] || // Initialisierung des Stapels
α := [a,a,b,b] // das Eingabewort
OPERATIONS
// die Operationen Schritt und LambdaSchritt modellieren
// Schritte in der Ableitungsrelation
Schritt(z‘,s) = PRE α ≠ ∅ ∧ γ ≠ ∅ ∧
z‘↦s ∈ δ[{(z,first(α),first(γ))}] THEN
z := z‘ || // in den neuen Zustand wechseln
α := tail(α) || // das erste Symbol auf der Eingabe löschen
γ := s^tail(γ) // s auf den Stapel packen
END;
LambdaSchritt(z‘,s) = PRE γ ≠ ∅ ∧
z‘↦s ∈ δ[{(z,lambda,first(γ))}] THEN
z := z‘ || // in den neuen Zustand wechseln
γ := s^tail(γ) // s auf den Stapel packen
END;
Akzeptieren = PRE γ = ∅ ∧ α = ∅ THEN
/* Wir akzeptieren wenn Eingabe und Stapel leer sind */
skip END
END
```
%% Output
Loaded machine: PDA
%% Cell type:code id: tags:
```
prob
:constants
```
%% Output
Machine constants set up using operation 0: $setup_constants()
%% Cell type:code id: tags:
```
prob
:init
```
%% Output
Machine initialised using operation 1: $initialise_machine()
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">BOT</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
Schritt(z0,
{(1|->A),(2|->
BOT
)}
)
Schritt(z0,
[A,
BOT
]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{(1|->A),(2|->
BOT
)}
)
Executed operation: Schritt(z0,
[A,
BOT
]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">A</td>
<td style="padding:10px">BOT</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
(z,α,γ)
```
%% Output
$(\mathit{z0}\mapsto
\{(1\mapsto \mathit{a}),(2\mapsto \mathit{b}),(3\mapsto \mathit{b})\}\mapsto\{(1\mapsto \mathit{A}),(2\mapsto \mathit{BOT})\}
)$
(z0↦
{(1↦a),(2↦b),(3↦b)}↦{(1↦A),(2↦
BOT
)}
)
$(\mathit{z0}\mapsto
[a,\mathit{b},b]\mapsto [A,BOT]
)$
(z0↦
[a,b,b]↦[A,
BOT
]
)
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
Schritt(z0,
{(1|->A),(2|->A)}
)
Schritt(z0,
[A,A]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{(1|->A),(2|->A)}
)
Executed operation: Schritt(z0,
[A,A]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">A</td>
<td style="padding:10px">A</td>
<td style="padding:10px">BOT</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
Schritt(z1,
{}
)
Schritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z1,
{}
)
Executed operation: Schritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z1</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">b</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">A</td>
<td style="padding:10px">BOT</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
Schritt(z1,
{}
)
Schritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z1,
{}
)
Executed operation: Schritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z1</td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">BOT</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
LambdaSchritt(z1,
{}
)
LambdaSchritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:exec LambdaSchritt
```
%% Output
Executed operation: LambdaSchritt(z1,
{}
)
Executed operation: LambdaSchritt(z1,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z1</td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Sets: Z, SYMBOLE
Constants: δ
Variables: z, α, γ
Operations:
Akzeptieren()
%% Cell type:code id: tags:
```
prob
:exec Akzeptieren
```
%% Output
Executed operation: Akzeptieren()
%% Cell type:markdown id: tags:
Das Eingabewort
``aabb``
wurde akzeptiert.
%% Cell type:markdown id: tags:
## PDA für eine kfG
Aus einer kontextfreien Grammatik kann man einen PDA konstruieren der die gleiche Sprache akzeptiert.
%% Cell type:code id: tags:
```
prob
::load
MACHINE PDA
MACHINE PDA
_für_kfG
/* B Modell eines PDA */
SETS
Z = {z0}; // die Zustände des Automaten, z0 ist der Startzustand
SYMBOLE={a,b, S, C, lambda} /* BOT = # = Bottom-Symbol im Keller*/
DEFINITIONS
Σ == {a,b}; // das Eingabe-Alphabet
BOT == S;
Γ == {S,C}; // das Kelleralphabet
ANIMATION_FUNCTION_DEFAULT == {(1,1,z)};
ANIMATION_FUNCTION == {2}*α ∪ {3}*(γ);
ANIMATION_FUNCTION1 == {(1,0,"z: "),(2,0,"α:"),(3,0,"γ:")};
ANIMATION_STR_JUSTIFY_LEFTx == TRUE;
SET_PREF_P
RETTY_PRINT
_SEQUENCES == TRUE
SET_PREF_P
P
_SEQUENCES == TRUE
CONSTANTS P, δ
PROPERTIES
/* Die Grammatik Regeln */
P = { S ↦ [a,S,b], S ↦ [C],
C ↦ [a,b] } ∧
/* Berechnung von δ aus P */
δ = /* lässt sich eine Regel auf das Top-Symbol im Keller anwenden tue
dies ohne etwas zu lesen :*/
{ lhs,rhs | ∃(A,q).( A↦q ∈ P ∧ lhs=(z0,lambda,A) ∧ rhs=(z0,q))}
∪
/* ist das Top-Symbol im Keller ein Terminalzeichen a welches
auf der Eingabe steht, so wird dies aus dem Keller gePOPt */
{ lhs,rhs | ∃a.(a∈Σ ∧ lhs = (z0,a,a) & rhs = (z0,[]))}
VARIABLES
z, α, γ // Konfiguration in dem sich der PDA befindet
INVARIANT
z ∈ Z ∧ // der aktuelle Zustand
α ∈ seq(Σ) ∧ // der noch zu lesende Teil des Eingabeworts
γ ∈ seq(Γ) // aktuelle Kellerinhalt
INITIALISATION
z := z0 ||
γ := [BOT] || // Initialisierung des Stapels
α := [a,a,b,b] // das Eingabewort
OPERATIONS
// die Operationen Schritt und LambdaSchritt modellieren
// Schritte in der Ableitungsrelation
Schritt(z‘,s) = PRE α ≠ ∅ ∧ γ ≠ ∅ ∧
z‘↦s ∈ δ[{(z,first(α),first(γ))}] THEN
z := z‘ || // in den neuen Zustand wechseln
α := tail(α) || // das erste Symbol auf der Eingabe löschen
γ := s^tail(γ) // s auf den Stapel packen
END;
LambdaSchritt(z‘,s) = PRE γ ≠ ∅ ∧
z‘↦s ∈ δ[{(z,lambda,first(γ))}] THEN
z := z‘ || // in den neuen Zustand wechseln
γ := s^tail(γ) // s auf den Stapel packen
END;
Akzeptieren = PRE γ = ∅ ∧ α = ∅ THEN
/* Wir akzeptieren wenn Eingabe und Stapel leer sind */
skip END
END
```
%% Output
Loaded machine: PDA
Loaded machine: PDA
_für_kfG
%% Cell type:code id: tags:
```
prob
:constants
```
%% Output
Machine constants set up using operation 0: $setup_constants()
%% Cell type:code id: tags:
```
prob
:init
```
%% Output
Machine initialised using operation 1: $initialise_machine()
%% Cell type:code id: tags:
```
prob
:table {z,x,X,z2,Xs| ((z,x,X)↦(z2,Xs)) : δ}
```
%% Output
|z|x|X|z2|Xs|
|---|---|---|---|---|
|$\
renewcommand{\emptyset}{\mathord\varnothing}\renewcommand{\emptyset}{\mathord\varnothing}\renewcommand{\emptyset}{\mathord\varnothing}\renewcommand{\emptyset}{\mathord\varnothing}\renewcommand{\emptyset}{\mathord\varnothing}\
mathit{z0}$|$\mathit{a}$|$\mathit{a}$|$\mathit{z0}$|$
\emptyset
$|
|$\mathit{z0}$|$\mathit{b}$|$\mathit{b}$|$\mathit{z0}$|$
\emptyset
$|
|$\mathit{z0}$|$\mathit{S}$|$\mathit{S}$|$\mathit{z0}$|$
\emptyset
$|
|$\mathit{z0}$|$\mathit{C}$|$\mathit{C}$|$\mathit{z0}$|$
\emptyset
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{S}$|$\mathit{z0}$|$
\{(1\mapsto \mathit{C})\}
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{S}$|$\mathit{z0}$|$
\{(1\mapsto \mathit{a}),(2\mapsto \mathit{S}),(3\mapsto \mathit{b})\}
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{C}$|$\mathit{z0}$|$
\{(1\mapsto \mathit{a}),(2\mapsto \mathit{b})\}
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{lambda}$|$\mathit{z0}$|$
\emptyset
$|
|$\mathit{z0}$|$\mathit{a}$|$\mathit{a}$|$\mathit{z0}$|$
[]
$|
|$\mathit{z0}$|$\mathit{b}$|$\mathit{b}$|$\mathit{z0}$|$
[]
$|
|$\mathit{z0}$|$\mathit{S}$|$\mathit{S}$|$\mathit{z0}$|$
[]
$|
|$\mathit{z0}$|$\mathit{C}$|$\mathit{C}$|$\mathit{z0}$|$
[]
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{S}$|$\mathit{z0}$|$
[C]
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{S}$|$\mathit{z0}$|$
[a,\mathit{S},b]
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{C}$|$\mathit{z0}$|$
[a,b]
$|
|$\mathit{z0}$|$\mathit{lambda}$|$\mathit{lambda}$|$\mathit{z0}$|$
[]
$|
z x X z2 Xs
z0 a a z0
{}
z0 b b z0
{}
z0 S S z0
{}
z0 C C z0
{}
z0 lambda S z0
{(1|->C)}
z0 lambda S z0
{(1|->a),(2|->S),(3|->b)}
z0 lambda C z0
{(1|->a),(2|->b)}
z0 lambda lambda z0
{}
z0 a a z0
[]
z0 b b z0
[]
z0 S S z0
[]
z0 C C z0
[]
z0 lambda S z0
[C]
z0 lambda S z0
[a,S,b]
z0 lambda C z0
[a,b]
z0 lambda lambda z0
[]
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">S</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Machine: PDA
_für_kfG
Sets: Z, SYMBOLE
Constants: P, δ
Variables: z, α, γ
Operations:
LambdaSchritt(z0,
{(1|->C)}
)
LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)
LambdaSchritt(z0,
[C]
)
LambdaSchritt(z0,
[a,S,b]
)
%% Cell type:code id: tags:
```
prob
:exec LambdaSchritt s = [a,S,b]
```
%% Output
Executed operation: LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)
Executed operation: LambdaSchritt(z0,
[a,S,b]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">S</td>
<td style="padding:10px">b</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Machine: PDA
_für_kfG
Sets: Z, SYMBOLE
Constants: P, δ
Variables: z, α, γ
Operations:
Schritt(z0,
{}
)
Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{}
)
Executed operation: Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">S</td>
<td style="padding:10px">b</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Machine: PDA
_für_kfG
Sets: Z, SYMBOLE
Constants: P, δ
Variables: z, α, γ
Operations:
LambdaSchritt(z0,
{(1|->C)}
)
LambdaSchritt(z0,
{(1|->a),(2|->S),(3|->b)}
)
LambdaSchritt(z0,
[C]
)
LambdaSchritt(z0,
[a,S,b]
)
%% Cell type:code id: tags:
```
prob
:exec LambdaSchritt s = [C]
```
%% Output
Executed operation: LambdaSchritt(z0,
{(1|->C)}
)
Executed operation: LambdaSchritt(z0,
[C]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">C</td>
<td style="padding:10px">b</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Machine: PDA
_für_kfG
Sets: Z, SYMBOLE
Constants: P, δ
Variables: z, α, γ
Operations:
LambdaSchritt(z0,
{(1|->a),(2|->b)}
)
LambdaSchritt(z0,
[a,b]
)
%% Cell type:code id: tags:
```
prob
:exec LambdaSchritt s=[a,b]
```
%% Output
Executed operation: LambdaSchritt(z0,
{(1|->a),(2|->b)}
)
Executed operation: LambdaSchritt(z0,
[a,b]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">a</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:browse
```
%% Output
Machine: PDA
Machine: PDA
_für_kfG
Sets: Z, SYMBOLE
Constants: P, δ
Variables: z, α, γ
Operations:
Schritt(z0,
{}
)
Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{}
)
Executed operation: Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">b</td>
<td style="padding:10px">b</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{}
)
Executed operation: Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:10px">b</td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:10px">b</td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:exec Schritt
```
%% Output
Executed operation: Schritt(z0,
{}
)
Executed operation: Schritt(z0,
[]
)
%% Cell type:code id: tags:
```
prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
<tr>
<td style="padding:10px">z: </td>
<td style="padding:10px">z0</td>
</tr>
<tr>
<td style="padding:10px">α:</td>
<td style="padding:0px"></td>
</tr>
<tr>
<td style="padding:10px">γ:</td>
<td style="padding:0px"></td>
</tr>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
```
prob
:exec Akzeptieren
```
%% Output
Executed operation: Akzeptieren()
%% Cell type:markdown id: tags:
Das Wort
``aabb``
wird sowohl von der Grammatik generiert als auch von diesem generierten PDA akzeptiert.
%% Cell type:code id: tags:
```
prob
```
...
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