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Recent questions tagged peter-linz
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91
Peter Linz Edition 4 Exercise 6.1 Question 14 (Page No. 162)
Suppose that $G$ is a context-free grammar for which $λ ∈ L (G)$. Show that if we apply the construction in Theorem 6.3, we obtain a new grammar $\widehat{G}$ such that $L(\widehat{G} ) = L (G) –$ {$λ$}.
Naveen Kumar 3
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Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
196
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peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
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1
answer
92
Peter Linz Edition 4 Exercise 6.1 Question 12 (Page No. 162)
Remove $λ$-productions from the grammar with productions $S\rightarrow aSb|SS|\lambda.$ What language does the resulting grammar generate?
Naveen Kumar 3
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in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
244
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peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
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93
Peter Linz Edition 4 Exercise 6.1 Question 11 (Page No. 162)
Complete the proof of Theorem 6.4. Theorem 6.4 Let $G = (V, T, S, P )$ be any context-free grammar without $λ$-productions. Then there exists a context-free grammar $\widehat{G}=(\widehat{V},\widehat{T},S,\widehat{P})$ that does not have any unit-productions and that is equivalent to $G$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
278
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
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0
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94
Peter Linz Edition 4 Exercise 6.1 Question 10 (Page No. 162)
Complete the proof of Theorem 6.3. Theorem 6.3 Let $G$ be any context-free grammar with $λ$ not in $L (G)$. Then there exists an equivalent grammar $\widehat{G}$ having no $λ$-productions.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
261
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
1
vote
1
answer
95
Peter Linz Edition 4 Exercise 6.1 Question 8 (Page No. 162)
Remove all unit-productions, all useless productions, and all λ-productions from the grammar $S\rightarrow aA|aBB,$ $A\rightarrow aaA|\lambda,$ $B\rightarrow bB|bbC,$ $C\rightarrow B.$ What language does this grammar generate?
Naveen Kumar 3
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in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
2.2k
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
context-free-language
1
vote
1
answer
96
Peter Linz Edition 4 Exercise 6.1 Question 7 (Page No. 162)
Eliminate all λ-productions from $S\rightarrow AaB|aaB,$ $A\rightarrow \lambda,$ $B\rightarrow bbA|\lambda.$
Naveen Kumar 3
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in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
385
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
1
vote
2
answers
97
Peter Linz Edition 4 Exercise 6.1 Question 6 (Page No. 161)
Eliminate useless productions from $S\rightarrow a|aA|B|C,$ $A\rightarrow aB|\lambda,$ $B\rightarrow Aa,$ $C\rightarrow cCD,$ $D\rightarrow ddd.$
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
494
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
1
vote
1
answer
98
Peter Linz Edition 4 Exercise 6.1 Question 5 (Page No. 161)
Eliminate all useless productions from the grammar $S\rightarrow aS|AB,$ $A\rightarrow bA,$ $B\rightarrow AA.$ What language does this grammar generate?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
365
views
peter-linz
peter-linz-edition4
context-free-grammar
context-free-language
0
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99
Peter Linz Edition 4 Exercise 6.1 Question 4 (Page No. 161)
In Theorem 6.1, why is it necessary to assume that $A$ and $B$ are different variables?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
284
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
0
votes
0
answers
100
Peter Linz Edition 4 Exercise 6.1 Question 3 (Page No. 161)
Show that the two grammars $S\rightarrow abAB|ba,$ $A\rightarrow aaa,$ $B\rightarrow aA|bb$ and $S\rightarrow abAaA|abAbb|ba,$ $A\rightarrow aaa$ are equivalent.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
185
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
0
votes
0
answers
101
Peter Linz Edition 4 Exercise 6.1 Question 2 (Page No. 161)
Show a derivation tree for the string $ababbac$, using grammar with productions $A\rightarrow a|aaA|abBC,$ $B\rightarrow abbA|b.$ also show the derivation tree for grammar with productions $A\rightarrow a|aaA|ababbAc|abbc,$ $B\rightarrow abbA|b.$
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
144
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
0
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0
answers
102
Peter Linz Edition 4 Exercise 6.1 Question 1 (Page No. 161)
Complete the proof of Theorem 6.1 by showing that $S\overset{*}{\Rightarrow}_{\widehat{G}} w$ implies $S\overset{*}{\Rightarrow}_{G} w$. Theorem 6.1 Let $G = (V, T, S, P)$ be a context-free grammar. Suppose that $P$ ... $P$, and adding to it $A\rightarrow x_1y_1x_2|x_1y_2x_2|...|x_1y_nx_2.$ Then, $L(\widehat{G})=L(G)$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 15, 2019
by
Naveen Kumar 3
520
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
0
votes
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answers
103
Peter Linz Edition 5 Exercise 8.1 Question 7(k) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free $L = \{a^nb^m: \text{n is prime and m is not prime}\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
351
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
1
answer
104
Peter Linz Edition 5 Exercise 8.1 Question 7(j) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free $L = \{a^nb^m:\text{n is prime or m is prime}\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
340
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
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105
Peter Linz Edition 5 Exercise 8.1 Question 7(i) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free $L = \{a^nb^m: \text{n and m are both prime}\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
192
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
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106
Peter Linz Edition 5 Exercise 8.1 Question 7(h) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L = \{w\in\{a,b,c\}^*:n_a(w)+n_b(w)=2n_c(w),n_a(w) = n_b(w)\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
289
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
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107
Peter Linz Edition 5 Exercise 8.1 Question 7(g) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L=\{w:n_a(w)/n_b(w) = n_c(w)\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
170
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
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108
Peter Linz Edition 5 Exercise 8.1 Question 7(f) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L = \{w:n_a(w) <n_b(w)<n_c(w)\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
216
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
answers
109
Peter Linz Edition 5 Exercise 8.1 Question 7(e) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L= \{a^nb^jc^k:n<j,n\leq k \leq j\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
272
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
answers
110
Peter Linz Edition 5 Exercise 8.1 Question 7(d) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L=\{a^nb^jc^k : k>n,k>j\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
186
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
2
answers
111
Peter Linz Edition 5 Exercise 8.1 Question 7(c) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L = \{a^nb^jc^k:k=jn\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
455
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
answers
112
Peter Linz Edition 5 Exercise 8.1 Question 7(b) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L = \{a^nb^j: n\geq(j-1)^3\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
143
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
1
vote
0
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113
Peter Linz Edition 5 Exercise 8.1 Question 7(a) (Page No. 212)
Show that the following languages on $\Sigma = \{a,b,c\}$ are not context-free. $L = \{a^nb^j : n\leq j^2\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
278
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
0
votes
0
answers
114
Peter Linz Edition 5 Exercise 8.1 Question 6 (Page No. 212)
Show that the language $L = \Big\{ a^{n^2} :n\geq 0\Big\}$ is not context free.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
299
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
context-free-language
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votes
0
answers
115
Peter Linz Edition 5 Exercise 8.1 Question 5 (Page No. 212)
Is the language $L = \{a^nb^m:n=2^m\}$ context free$?$
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
239
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
context-free-language
0
votes
0
answers
116
Peter Linz Edition 5 Exercise 8.1 Question 4 (Page No. 212)
Show that $L=\{w \in \{a,b,c\}^*:n_a^2(w) + n_b^2(w) = n_c^2(w)\}$ is not a context-free.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
145
views
peter-linz
peter-linz-edition5
theory-of-computation
proof
pumping-lemma
0
votes
0
answers
117
Peter Linz Edition 5 Exercise 8.1 Question 3 (Page No. 212)
Show that $L=\{ww^Rw:w\in\{a,b\}^*\}$ is not a context-free language.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
176
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
0
votes
0
answers
118
Peter Linz Edition 5 Exercise 8.1 Question 2 (Page No. 212)
Show that the language $L = \{a^n : n \text{ is a prime number}\}$ is not context-free.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
127
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
0
votes
0
answers
119
Peter Linz Edition 5 Exercise 8.1 Question 1 (Page No. 212)
Show that the language $L = \{w\in \{a,b,c\}^*: n_a(w) = n_b(w) \leq n_c(w)\}$ is not context-free.
Rishi yadav
asked
in
Theory of Computation
Apr 15, 2019
by
Rishi yadav
144
views
peter-linz
peter-linz-edition5
theory-of-computation
pumping-lemma
proof
2
votes
1
answer
120
Peter Linz Edition 4 Exercise 5.2 Question 20 (Page No. 145)
Find a grammar equivalent to $S\rightarrow aAB, A\rightarrow bBb, B\rightarrow A|\lambda$ that satisfies the conditions of Theorem 5.2. Theorem 5.2 Suppose that $G = (V, T, S, P)$ is a context-free grammar that does not have ... algorithm which, for any $w ∈ Σ^*,$ either produces a parsing of $w$ or tells us that no parsing is possible.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 14, 2019
by
Naveen Kumar 3
364
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-grammar
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