From 92a368fd798bbad321053fc024afa538c97f8f96 Mon Sep 17 00:00:00 2001
From: Chris <Christopher.Happe@uni-duesseldorf.de>
Date: Wed, 14 Oct 2020 12:33:30 +0200
Subject: [PATCH] Neue Maschiene zur Visualisierung der Chomsky-Hierarchie
---
info4/kapitel-1/Grammatiken.ipynb | 855 +++++++++++++++++++-----------
1 file changed, 551 insertions(+), 304 deletions(-)
diff --git a/info4/kapitel-1/Grammatiken.ipynb b/info4/kapitel-1/Grammatiken.ipynb
index ea71fb5..be926db 100644
--- a/info4/kapitel-1/Grammatiken.ipynb
+++ b/info4/kapitel-1/Grammatiken.ipynb
@@ -29,7 +29,7 @@
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -38,7 +38,7 @@
"Loaded machine: Grammatik"
]
},
- "execution_count": 4,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -65,7 +65,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -74,7 +74,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 5,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -85,7 +85,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -103,7 +103,7 @@
"\tRHS = []"
]
},
- "execution_count": 6,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -121,7 +121,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -133,7 +133,7 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 7,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -159,7 +159,7 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
@@ -168,7 +168,7 @@
"Loaded machine: Grammatik"
]
},
- "execution_count": 8,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -199,7 +199,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -208,7 +208,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 9,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -226,7 +226,7 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -238,7 +238,7 @@
"/*@symbolic*/ {u,v∣∃(x,z,p,q)·(p ↦ q ∈ {([S]↦[]),([S]↦[a,S,b])} ∧ u = x ⌒ p ⌒ z ∧ v = x ⌒ q ⌒ z)}"
]
},
- "execution_count": 10,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -249,7 +249,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -261,7 +261,7 @@
"TRUE"
]
},
- "execution_count": 14,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -272,7 +272,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -284,7 +284,7 @@
"FALSE"
]
},
- "execution_count": 12,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -295,7 +295,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -313,7 +313,7 @@
"\tx = []"
]
},
- "execution_count": 15,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -331,7 +331,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -343,7 +343,7 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 16,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -354,7 +354,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -366,7 +366,7 @@
"{[a,b,S],[a,S,b],[a,S,b,a,S,b],[a,a,S,b,b,S]}"
]
},
- "execution_count": 18,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -384,7 +384,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -396,7 +396,7 @@
"{[a,b],[a,a,S,b,b]}"
]
},
- "execution_count": 19,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -407,7 +407,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -419,7 +419,7 @@
"{[a,a,b,b],[a,a,a,S,b,b,b]}"
]
},
- "execution_count": 20,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -443,7 +443,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -455,7 +455,7 @@
"TRUE"
]
},
- "execution_count": 23,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -473,7 +473,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -485,7 +485,7 @@
"{[S]}"
]
},
- "execution_count": 24,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -496,7 +496,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -508,7 +508,7 @@
"{[],[a,S,b]}"
]
},
- "execution_count": 25,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -519,7 +519,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -531,7 +531,7 @@
"{[a,b],[a,a,S,b,b]}"
]
},
- "execution_count": 26,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -542,7 +542,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -554,7 +554,7 @@
"{[a,a,b,b],[a,a,a,S,b,b,b]}"
]
},
- "execution_count": 27,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -565,7 +565,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -577,7 +577,7 @@
"{[a,a,a,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 28,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -600,7 +600,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
@@ -612,7 +612,7 @@
"{[],[a,b],[S],[a,a,b,b],[a,S,b],[a,a,a,b,b,b],[a,a,S,b,b],[a,a,a,S,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 29,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -630,7 +630,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
@@ -642,7 +642,7 @@
"{[],[a,b],[a,a,b,b],[a,a,a,b,b,b]}"
]
},
- "execution_count": 30,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -660,7 +660,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 23,
"metadata": {},
"outputs": [
{
@@ -672,7 +672,7 @@
"{[],[a,b],[S],[a,a,b,b],[a,S,b],[a,a,a,b,b,b],[a,a,S,b,b],[a,a,a,S,b,b,b],[a,a,a,a,S,b,b,b,b]}"
]
},
- "execution_count": 31,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -683,7 +683,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
@@ -692,7 +692,7 @@
"Preference changed: DOT_DECOMPOSE_NODES = FALSE\n"
]
},
- "execution_count": 32,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -703,7 +703,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 25,
"metadata": {},
"outputs": [
{
@@ -712,106 +712,123 @@
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- "<!-- Generated by graphviz version 2.28.0 (20110509.1545)\n",
+ "<!-- Generated by graphviz version 2.44.1 (0)\n",
" -->\n",
"<!-- Title: state Pages: 1 -->\n",
- "<svg width=\"354pt\" height=\"404pt\"\n",
- " viewBox=\"0.00 0.00 354.00 404.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
- "<g id=\"graph1\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 400)\">\n",
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@@ -820,7 +837,7 @@
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]
},
- "execution_count": 33,
+ "execution_count": 25,
"metadata": {},
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}
@@ -838,7 +855,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 26,
"metadata": {},
"outputs": [
{
@@ -847,7 +864,7 @@
"Loaded machine: Grammatik2"
]
},
- "execution_count": 34,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -883,7 +900,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
@@ -892,7 +909,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 35,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -903,7 +920,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -915,7 +932,7 @@
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]
},
- "execution_count": 36,
+ "execution_count": 28,
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@@ -926,7 +943,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 29,
"metadata": {},
"outputs": [
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@@ -938,7 +955,7 @@
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]
},
- "execution_count": 37,
+ "execution_count": 29,
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}
@@ -949,7 +966,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -958,7 +975,7 @@
"Preference changed: DOT_DECOMPOSE_NODES = FALSE\n"
]
},
- "execution_count": 38,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -969,7 +986,7 @@
},
{
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- "execution_count": 39,
+ "execution_count": 31,
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@@ -1236,7 +1297,7 @@
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]
},
- "execution_count": 39,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -1247,7 +1308,7 @@
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
@@ -1289,9 +1350,23 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 33,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{([a,B]\\mapsto [a,b]),([b,B]\\mapsto [b,b]),([b,C]\\mapsto [b,c]),([c,C]\\mapsto [c,c]),([S]\\mapsto [a,\\mathit{S},\\mathit{B},C]),([S]\\mapsto [a,\\mathit{B},C]),([C,B]\\mapsto [B,C])\\}$"
+ ],
+ "text/plain": [
+ "{([a,B]↦[a,b]),([b,B]↦[b,b]),([b,C]↦[b,c]),([c,C]↦[c,c]),([S]↦[a,S,B,C]),([S]↦[a,B,C]),([C,B]↦[B,C])}"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"P"
]
@@ -1306,7 +1381,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 34,
"metadata": {},
"outputs": [
{
@@ -1318,7 +1393,7 @@
"TRUE"
]
},
- "execution_count": 42,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -1329,7 +1404,7 @@
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 35,
"metadata": {},
"outputs": [
{
@@ -1341,7 +1416,7 @@
"{([a,B]↦[a,b]),([b,B]↦[b,b]),([b,C]↦[b,c]),([c,C]↦[c,c]),([S]↦[a,S,B,C]),([S]↦[a,B,C]),([C,B]↦[B,C])}"
]
},
- "execution_count": 41,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -1359,7 +1434,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 36,
"metadata": {},
"outputs": [
{
@@ -1371,7 +1446,7 @@
"FALSE"
]
},
- "execution_count": 43,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -1390,7 +1465,7 @@
},
{
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- "execution_count": 44,
+ "execution_count": 37,
"metadata": {},
"outputs": [
{
@@ -1417,7 +1492,7 @@
},
{
"cell_type": "code",
- "execution_count": 45,
+ "execution_count": 38,
"metadata": {},
"outputs": [
{
@@ -1429,7 +1504,7 @@
"{([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 45,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
@@ -1440,7 +1515,7 @@
},
{
"cell_type": "code",
- "execution_count": 46,
+ "execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1458,7 +1533,7 @@
"\tP1 = {([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 46,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -1476,7 +1551,7 @@
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 40,
"metadata": {},
"outputs": [
{
@@ -1488,7 +1563,7 @@
"FALSE"
]
},
- "execution_count": 47,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -1499,7 +1574,7 @@
},
{
"cell_type": "code",
- "execution_count": 48,
+ "execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -1521,7 +1596,7 @@
"\tP1 = {([S]↦[]),([S]↦[a,S,b])}"
]
},
- "execution_count": 48,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
@@ -1560,6 +1635,178 @@
"* $REG \\subseteq CF \\subseteq CS \\subseteq \\mathfrak{L}_0.$"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: Chomsky"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE Chomsky\n",
+ "SETS ΣN = {a, b, c, S, A, B, C}\n",
+ "CONSTANTS Σ, N, P0, P1, P2, P3, P4, Grammatiken\n",
+ "PROPERTIES\n",
+ " Σ = {a, b, c} ∧\n",
+ " N = {S, A, B, C} ∧\n",
+ " Σ ∩ N = {} ∧\n",
+ " Σ ∪ N = ΣN ∧\n",
+ " //L0 = {x∈{a, b}^* | x enthält gleich viele as und bs}\n",
+ " //Ohne Sonderrregelung für lambda ist L0 von Typ 0.\n",
+ " P0 = {([S] ↦ [a, b]), ([S] ↦ [S, S]), ([S] ↦ []), ([a, b] ↦ [b, a]), ([b, a] ↦ [a, b])} ∧\n",
+ " //L1 = {a^mb^mc^m | m≥1}\n",
+ " P1 = {([S] ↦ [S, S]), ([S] ↦ [A, B, C]), ([B, A] ↦ [A, B]), ([C, A] ↦ [A, C]), ([C, B] ↦ [B, C]),\n",
+ " ([A] ↦ [a]), ([a, B] ↦ [a, b]), ([b, B] ↦ [b, b]), ([b, C] ↦ [b, c]), ([c, C] ↦ [c, c])} ∧\n",
+ " //L2 = {x∈{a, b}^+ | x enthält gleich viele as und bs}\n",
+ " P2 = {([S] ↦ [A, B]), ([S] ↦ [B, A]),\n",
+ " ([A] ↦ [A, A, B]), ([A] ↦ [A, B, A]), ([A] ↦ [B, A, A]), ([A] ↦ [a]),\n",
+ " ([B] ↦ [B, B, A]), ([B] ↦ [B, A, B]), ([B] ↦ [A, B, B]), ([B] ↦ [b])} ∧\n",
+ " //L3 = L4 = {a, b, c}\n",
+ " P3 = {([S] ↦ [a]), ([S] ↦ [b]), ([S] ↦ [c])} ∧\n",
+ " P4 = {([S] ↦ [A, A]), ([A, A] ↦ [a]), ([S] ↦ [b]), ([S] ↦ [c])} ∧\n",
+ " Grammatiken = [P0, P1, P2, P3, P4]\n",
+ " \n",
+ "DEFINITIONS\n",
+ " SET_PREF_PP_SEQUENCES == TRUE;\n",
+ " L0(R) == TRUE; //Jede Grammatik ist vom Typ 0\n",
+ " L1(R) == IF ∀(p,q).( p↦q ∈ R ⇒ size(p) ≤ size(q)) THEN L0(R) ELSE FALSE END;\n",
+ " L2(R) == IF ∀(p,q).( p↦q ∈ R ⇒ size(p)=1 & p∈seq(N)) THEN L1(R) ELSE FALSE END;\n",
+ " L3(R) == IF ∀(p,q).( p↦q ∈ R ⇒ size(q)>0 & size(q) ≤ 2 & first(q)∈Σ & (size(q)≤1 or first(tail(q))∈N)) THEN L2(R) ELSE FALSE END;\n",
+ " \n",
+ " \"LibraryStrings.def\";\n",
+ " ANIMATION_FUNCTION_DEFAULT == {(0,0,\"P\"), (1,0,\"P0\"), (2,0,\"P1\"), (3,0,\"P2\"), (4,0,\"P3\"), (5,0,\"P4\")};\n",
+ " ANIMATION_FUNCTION1 == {c,r,i| r=1 ∧ c∈dom(Grammatiken) ∧ i=TO_STRING(L0(Grammatiken(c)))} ∪ {(0,1,\"L0(P)\")};\n",
+ " ANIMATION_FUNCTION2 == {c,r,i| r=2 ∧ c∈dom(Grammatiken) ∧ i=TO_STRING(L1(Grammatiken(c)))} ∪ {(0,2,\"L1(P)\")};\n",
+ " ANIMATION_FUNCTION3 == {c,r,i| r=3 ∧ c∈dom(Grammatiken) ∧ i=TO_STRING(L2(Grammatiken(c)))} ∪ {(0,3,\"L2(P)\")};\n",
+ " ANIMATION_FUNCTION4 == {c,r,i| r=4 ∧ c∈dom(Grammatiken) ∧ i=TO_STRING(L3(Grammatiken(c)))} ∪ {(0,4,\"L3(P)\")};\n",
+ "END"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine constants set up using operation 0: $setup_constants()"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":constants"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine initialised using operation 1: $initialise_machine()"
+ ]
+ },
+ "execution_count": 44,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":init"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "<table style=\"font-family:monospace\"><tbody>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P</td>\n",
+ "<td style=\"padding:10px\">L0(P)</td>\n",
+ "<td style=\"padding:10px\">L1(P)</td>\n",
+ "<td style=\"padding:10px\">L2(P)</td>\n",
+ "<td style=\"padding:10px\">L3(P)</td>\n",
+ "</tr>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P0</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "</tr>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P1</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "</tr>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P2</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "</tr>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P3</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "</tr>\n",
+ "<tr>\n",
+ "<td style=\"padding:10px\">P4</td>\n",
+ "<td style=\"padding:10px\">TRUE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "<td style=\"padding:10px\">FALSE</td>\n",
+ "</tr>\n",
+ "</tbody></table>"
+ ],
+ "text/plain": [
+ "<Animation function visualisation>"
+ ]
+ },
+ "execution_count": 45,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":show"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die obige Tabelle zeigt, in welche Sprachklasse die entsprechenden Grammatiken fallen. Dabei ist zu beachten, dass L3 = L4 ist, aber P3 und P4 unterschiedliche Typen haben. Die Sprache fällt allerdings immer in die größte Spracheklasse zu der es eine Grammatik gibt, die diese Sprache erzeugt. Also gilt $L4 ∈ \\mathfrak{L}_3 = REG$. Daher reicht die Angabe einer Grammatik nicht aus, um zu zeigen dass eine Sprache höchstens in einer der Klassen liegt. Um dies zu zeigen gibt es verschiedene Methoden, wie z.B. das Pumping-Lemma oder die Myhill-Nerode Relation."
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
--
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