diff --git a/info4/kapitel-3/PDA_nach_kfG.ipynb b/info4/kapitel-3/PDA_nach_kfG.ipynb
index a5f9cfc16864fb7d8eb15167d33c60f0d90f1bf2..bd2e7f740be66b4903ab1337bc310b9669767aaa 100644
--- a/info4/kapitel-3/PDA_nach_kfG.ipynb
+++ b/info4/kapitel-3/PDA_nach_kfG.ipynb
@@ -9,7 +9,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -18,7 +18,7 @@
"Loaded machine: PDA_to_CFG"
]
},
- "execution_count": 16,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
@@ -28,56 +28,61 @@
"MACHINE PDA_to_CFG\n",
"/* Translating a PDA to a CFG */\n",
"SETS\n",
- " STATES = {z0,z1, symbol}; \n",
+ " Z = {z0,z1, symbol}; \n",
" /* symbol: virtueller Zustand um S und andere Symbole in der Grammatik darzustellen */\n",
- " SYMBOLS={a,b, A, BOT, lambda, S} /* BOT = # = bottom of stack*/\n",
+ " SYMBOLE={a,b, A, BOT, lambda, S} /* BOT = # = Ende vom Keller */\n",
"DEFINITIONS\n",
- " CFG_Alphabet == (STATES*(SYMBOLS-{lambda})*STATES);\n",
+ " kfG_Alphabet == (Z*(SYMBOLE \\ {lambda})*Z);\n",
" Σ == {a,b};\n",
" Γ == {A,BOT};\n",
- " ANIMATION_FUNCTION1 == {r,c,i| r=1 ∧ c∈dom(cur) ∧ i=prj1(STATES,SYMBOLS)(prj1(STATES*SYMBOLS,STATES)(cur(c)))};\n",
- " ANIMATION_FUNCTION2 == {r,c,i| r=2 ∧ c∈dom(cur) ∧ i=prj2(STATES,SYMBOLS)(prj1(STATES*SYMBOLS,STATES)(cur(c)))};\n",
- " ANIMATION_FUNCTION3 == {r,c,i| r=3 ∧ c∈dom(cur) ∧ i=prj2(STATES*SYMBOLS,STATES)(cur(c))};\n",
- " ANIMATION_STR_JUSTIFY_LEFT == TRUE;\n",
- " SET_PREF_PP_SEQUENCES == TRUE;\n",
- " PDA_STATES == (STATES-{symbol});\n",
+ " PDA_Zustände == (Z-{symbol});\n",
"\n",
" SYMS(s) == IF (s=lambda) THEN [] ELSE [SYM(s)] END;\n",
- " SYM(s) == (symbol,s,symbol);\n",
- " TERMINALS == {x|∃t.(t∈Σ ∧ x=SYM(t))}\n",
- "CONSTANTS delta, Productions\n",
+ " SYM(s) == (symbol,s,symbol); // Darstellung eines Symbols als Tripel für die Grammatik\n",
+ " kfG_TERMINALE == {x|∃t.(t∈Σ ∧ x=SYM(t))};\n",
+ " \n",
+ " ANIMATION_FUNCTION1 == {r,c,i| r=1 ∧ c∈dom(cur) ∧ i=prj1(Z,SYMBOLE)(prj1(Z*SYMBOLE,Z)(cur(c)))};\n",
+ " ANIMATION_FUNCTION2 == {r,c,i| r=2 ∧ c∈dom(cur) ∧ i=prj2(Z,SYMBOLE)(prj1(Z*SYMBOLE,Z)(cur(c)))};\n",
+ " ANIMATION_FUNCTION3 == {r,c,i| r=3 ∧ c∈dom(cur) ∧ i=prj2(Z*SYMBOLE,Z)(cur(c))};\n",
+ " ANIMATION_STR_JUSTIFY_LEFT == TRUE;\n",
+ " SET_PREF_PP_SEQUENCES == TRUE\n",
+ "CONSTANTS δ, Regeln\n",
"PROPERTIES\n",
- " /* A PDA accepting {a^mb^m| m≥1} ; Beispiel von Info 4 (Folie 95ff) */\n",
- " delta = { (z0,a,BOT) ↦ (z0,[A,BOT]),\n",
+ " /* Ein PDA für {a^m b^m| m≥1} ; Beispiel von Info 4 (Folie 95ff) */\n",
+ " δ = { (z0,a,BOT) ↦ (z0,[A,BOT]),\n",
" (z0,a,A) ↦ (z0,[A,A]),\n",
" (z0,b,A) ↦ (z1,[]),\n",
" (z1,lambda,BOT) ↦ (z1,[]),\n",
" (z1,b,A) ↦ (z1,[]) } ∧\n",
"\n",
"\n",
- " Productions = /* Punkt 1 Folie 109 */\n",
- " { lhs,rhs | ∃z.(z∈PDA_STATES ∧ lhs=SYM(S) ∧ rhs = [(z0,BOT,z)])}\n",
+ " Regeln = /* Punkt 1 Folie 109 */\n",
+ " { lhs,rhs | ∃z.(z∈PDA_Zustände ∧ lhs=SYM(S) ∧ rhs = [(z0,BOT,z)])}\n",
" ∪\n",
" /* Punkt 2 Folie 109 */\n",
- " { lhs,rhs | ∃(z,a,A,z2).((z,a,A)↦(z2,[])∈delta ∧\n",
+ " { lhs,rhs | ∃(z,a,A,z2).((z,a,A)↦(z2,[])∈δ ∧\n",
" lhs=(z,A,z2) ∧ rhs = SYMS(a)) }\n",
" ∪\n",
" /* Punkt 3 Folie 110 */\n",
- " { lhs,rhs | ∃(z,a,A,B,z1,z2).((z,a,A)↦(z1,[B])∈delta ∧ z2∈PDA_STATES ∧\n",
+ " { lhs,rhs | ∃(z,a,A,B,z1,z2).((z,a,A)↦(z1,[B])∈δ ∧ z2∈PDA_Zustände ∧\n",
" lhs=(z,A,z2) ∧ rhs = SYMS(a)^[(z1,B,z2)]) }\n",
" ∪\n",
" /* Punkt 4 Folie 110 */\n",
- " { lhs,rhs | ∃(z,a,A,B,C,z1,z2,z3).((z,a,A)↦(z1,[B,C])∈delta ∧ \n",
- " z2∈PDA_STATES ∧ z3∈PDA_STATES ∧\n",
- " lhs=(z,A,z3) ∧ rhs = SYMS(a)^[(z1,B,z2),(z2,C,z3)]) }\n",
+ " { lhs,rhs | ∃(z,a,A,B,C,z1,z2,z3).((z,a,A)↦(z1,[B,C])∈δ ∧ \n",
+ " z2∈PDA_Zustände ∧ \n",
+ " z3∈PDA_Zustände ∧\n",
+ " lhs=(z,A,z3) ∧ \n",
+ " rhs = SYMS(a)^[(z1,B,z2),(z2,C,z3)]) }\n",
"VARIABLES cur\n",
"INVARIANT\n",
- " cur ∈ seq(CFG_Alphabet)\n",
- "INITIALISATION cur:=SYMS(S)\n",
+ " cur ∈ seq(kfG_Alphabet)\n",
+ "INITIALISATION\n",
+ " cur:=SYMS(S)\n",
"OPERATIONS\n",
- " ApplyRule(LHS,RHS,pre,post) = PRE LHS↦RHS ∈ Productions ∧\n",
+ " // Anwendung einer Grammatikregel\n",
+ " ApplyRule(LHS,RHS,pre,post) = PRE LHS↦RHS ∈ Regeln ∧\n",
" cur = pre^[LHS]^post ∧\n",
- " ran(pre) ⊆ TERMINALS /* Links Ableitung */\n",
+ " ran(pre) ⊆ kfG_TERMINALE /* Links Ableitung */\n",
" THEN\n",
" cur := pre^RHS^post\n",
" END\n",
@@ -86,7 +91,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -95,7 +100,7 @@
"Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 17,
+ "execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
@@ -106,7 +111,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 43,
"metadata": {},
"outputs": [
{
@@ -115,7 +120,7 @@
"Machine initialised using operation 1: $initialise_machine()"
]
},
- "execution_count": 18,
+ "execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
@@ -126,7 +131,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 45,
"metadata": {},
"outputs": [
{
@@ -138,18 +143,18 @@
"{(z0↦a↦A↦(z0↦[A,A])),(z0↦a↦BOT↦(z0↦[A,BOT])),(z0↦b↦A↦(z1↦[])),(z1↦b↦A↦(z1↦[])),(z1↦lambda↦BOT↦(z1↦[]))}"
]
},
- "execution_count": 37,
+ "execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "delta"
+ "δ"
]
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 46,
"metadata": {},
"outputs": [
{
@@ -171,7 +176,7 @@
"<Animation function visualisation>"
]
},
- "execution_count": 19,
+ "execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}