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Recent questions tagged context-free-language
0
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1
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121
Peter Linz Edition 4 Exercise 7.3 Question 10 (Page No. 200)
While the language in Exercise 9 is deterministic, the closely related language $L =$ {$ww^R : w ∈${$a,b$}$^*$} is known to be nondeterministic. Give arguments that make this statement plausible.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
322
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
1
answer
122
Peter Linz Edition 4 Exercise 7.3 Question 9 (Page No. 200)
Is the language {$wcw^R : w ∈ ${$a, b$}$^*$} deterministic?
Naveen Kumar 3
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in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
293
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peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
0
answers
123
Peter Linz Edition 4 Exercise 7.3 Question 8 (Page No. 200)
Is the language $L =$ {$a^nb^m : n = m$ or $n = m + 2$} deterministic?
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
237
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
0
answers
124
Peter Linz Edition 4 Exercise 7.3 Question 7 (Page No. 200)
Give reasons why one might conjecture that the following language is not deterministic. $L =$ { $a^nb^mc^k : n = m$ or $m = k$}.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
577
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
1
vote
1
answer
125
Peter Linz Edition 4 Exercise 7.3 Question 6 (Page No. 200)
For the language $L =$ {$a^nb^{2n} : n ≥ 0$}, show that $L^*$ is a deterministic context-free language.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
288
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
1
answer
126
Peter Linz Edition 4 Exercise 7.3 Question 4 (Page No. 200)
Is the language $L =$ {$a^nb^n : n ≥ 1$} $∪$ {$a$} deterministic?
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
301
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
1
vote
1
answer
127
Peter Linz Edition 4 Exercise 7.3 Question 3 (Page No. 200)
Is the language $L =$ {$a^nb^n : n ≥ 1$} $∪$ {$b$} deterministic?
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
298
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
0
answers
128
Peter Linz Edition 4 Exercise 7.3 Question 2 (Page No. 200)
Show that $L =$ {$a^nb^m : m ≥ n + 2$} is deterministic.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
177
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
0
votes
0
answers
129
Peter Linz Edition 4 Exercise 7.3 Question 1 (Page No. 200)
Show that $L =$ {$a^nb^{2n} : n ≥ 0$} is a deterministic context-free language.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 23, 2019
by
Naveen Kumar 3
205
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
2
votes
2
answers
130
Theory of Computation: Context Free Languages
Hi, I am having a doubt understanding the result of CFL - Regular: Here's my approach: CFL - Regular = CFL INTERSECTION Regular' = CFL INTERSECTION Regular = CFL Suppose some CFL L1= {a^n b^n | n>=1} and some Regular R1= (a+b)* ... to say CFL - Regular = Regular or CFL - Regular = CFL ? If both are separate options, which one should I go for? Thanks
DukeThunders
asked
in
Theory of Computation
Jun 9, 2019
by
DukeThunders
412
views
theory-of-computation
context-free-language
self-doubt
1
vote
2
answers
131
ACE Academy: Recognition of CFG
$L1 =\left \{ a^{m} b^{n} c^{p} | \left ( m \geq n \right )\text{or} \left ( n = p \right ) \right \}$ $L2 =\left \{ a^{m} b^{n} c^{p} | \left ( m \geq n \right )\text{and} \left ( n = p \right ) \right \}$ $(a)$ Both are NCFL’s $(b)$ L1 is DCFL and L2 is NCFL $(c)$ L1 is NCFL and L2 is not context-free $(d)$ Both are not context-free
Hirak
asked
in
Theory of Computation
May 22, 2019
by
Hirak
800
views
context-free-grammar
context-free-language
dcfl
0
votes
1
answer
132
self doubt: TOC
is union of regular language and context free language always regular?
Hirak
asked
in
Theory of Computation
May 22, 2019
by
Hirak
570
views
theory-of-computation
regular-language
context-free-language
3
votes
1
answer
133
Self Doubt : Ambiguity
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
logan1x
asked
in
Theory of Computation
May 10, 2019
by
logan1x
1.2k
views
theory-of-computation
finite-automata
ambiguous
regular-language
context-free-language
context
0
votes
0
answers
134
Michael Sipser Edition 3 Exercise 2 Question 37 (Page No. 158)
Prove the following stronger form of the pumping lemma, where in both pieces $v$ and $y$ must be nonempty when the string $s$ is broken up$.$If $A$ is a context-free language, then there is a number $k$ where, if $s$ is any string in $A$ of ... $i\geq 0,uv^{i}xy^{i}z\in A,$ $v\neq\epsilon$ and $y\neq\epsilon,$and $\mid vxy\mid\leq k.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
517
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
1
vote
1
answer
135
Michael Sipser Edition 3 Exercise 2 Question 36 (Page No. 158)
Give an example of a language that is not context free but that acts like a $CFL$ in the pumping lemma$.$ Prove that your example works$.$ $\text{(See the analogous example for regular languages in Question 54.)}$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.7k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
proof
0
votes
1
answer
136
Michael Sipser Edition 3 Exercise 2 Question 35 (Page No. 157)
Let $G$ be a $CFG$ in Chomsky normal form that contains $b$ variables$.$ Show that if $G$ generates some string with a derivation having at least $2^{b}$ steps$, L(G)$ is infinite$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
587
views
michael-sipser
theory-of-computation
context-free-language
conjunctive-normal-form
proof
1
vote
1
answer
137
Michael Sipser Edition 3 Exercise 2 Question 34 (Page No. 157)
Let $G = (V, \Sigma, R, S)$ be the following grammar. $V = \{S, T, U\}; \Sigma = \{0, \#\};$ and $R$ is the set of rules$:$ $S\rightarrow TT\mid U$ $T\rightarrow 0T\mid T0\mid \#$ ... existence of a pumping length $p$ for $B.$ What is the minimum value of $p$ that works in the pumping lemma$?$ Justify your answer$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.1k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
proof
0
votes
1
answer
138
Michael Sipser Edition 3 Exercise 2 Question 33 (Page No. 157)
Show that $F = \{a^{i}b^{j}\mid i = kj$ $\text{for some positive integer $k$\}}$ is not context free$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
252
views
michael-sipser
theory-of-computation
context-free-language
0
votes
2
answers
139
Michael Sipser Edition 3 Exercise 2 Question 32 (Page No. 157)
Let $\Sigma = \{1, 2, 3, 4\}$ and $C = \{w\in\Sigma^{*}\mid$ $\text{in }w,\text{ the number of }1\text{'s equals the number of }2\text{'s, and the number of } 3\text{'s equals the number of }4\text{'s}\}.$ Show that $C$ is not context free.
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
640
views
michael-sipser
theory-of-computation
context-free-language
proof
2
votes
1
answer
140
Michael Sipser Edition 3 Exercise 2 Question 31 (Page No. 157)
Let $B$ be the language of all palindromes over $\{0,1\}$ containing equal numbers of $0's$ and $1's.$ Show that $B$ is not context free$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.4k
views
michael-sipser
theory-of-computation
context-free-language
0
votes
1
answer
141
Michael Sipser Edition 3 Exercise 2 Question 30 (Page No. 157)
Use the pumping lemma to show that the following languages are not context free$.$ $\{0^{n}1^{n}0^{n}1^{n}\mid n\geq 0\}$ $\{0^{n}\#0^{2n}\#0^{3n}\mid n\geq 0\}$ $\{w\#t\mid w$ $\text{ is a substring of}$ $ t,$ $\text{where}$ ... $\text{each}$ $ t_{i}\in\{a,b\}^{*},$ $\text{and}$ $ t_{i}=t_{j}$ $\text{ for some}$ $ i\neq j\}$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.1k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
0
votes
0
answers
142
Michael Sipser Edition 3 Exercise 2 Question 29 (Page No. 157)
Show that the language $A=\{a^{i}b^{j}c^{k}\mid i=j$ $\text{or}$ $ j=k$ $\text{where}$ $ i,j,k\geq 0\}$ is inherently ambiguous$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
210
views
michael-sipser
theory-of-computation
context-free-language
inherently-ambiguous
0
votes
0
answers
143
Michael Sipser Edition 3 Exercise 2 Question 25 (Page No. 157)
For any language $A,$ let $SUFFIX(A) = \{v\mid uv \in A$ $\text{for some string u\}}.$ Show that the class of context-free languages is closed under the $\text{SUFFIX operation.}$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
377
views
michael-sipser
theory-of-computation
context-free-language
suffix-operation
proof
0
votes
1
answer
144
Michael Sipser Edition 3 Exercise 2 Question 24 (Page No. 157)
Let $E=\{a^{i}b^{j}\mid i\neq j$ $\text{and}$ $2i\neq j\}.$ Show that $E$ is a context-free language$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
217
views
michael-sipser
theory-of-computation
context-free-language
proof
0
votes
0
answers
145
Michael Sipser Edition 3 Exercise 2 Question 23 (Page No. 157)
Let $D = \{xy\mid x, y\in \{0,1\}^{*}$ $\text{and}$ $\mid x\mid = \mid y\mid$ $\text{but}$ $x\neq y\}.$ Show that $D$ is a context-free language$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
202
views
michael-sipser
theory-of-computation
context-free-language
proof
0
votes
1
answer
146
Michael Sipser Edition 3 Exercise 2 Question 21 (Page No. 156)
Let $\Sigma = \{a,b\}.$ Give a $CFG$ generating the language of strings with twice as many $a’s$ as $b’s.$ Prove that your grammar is correct$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
272
views
michael-sipser
theory-of-computation
context-free-grammar
context-free-language
0
votes
0
answers
147
Michael Sipser Edition 3 Exercise 2 Question 20 (Page No. 156)
Let $A/B = \{w\mid wx\in A$ $\text{for some}$ $x \in B\}.$ Show that if $A$ is context free and $B$ is regular$,$ then $A/B$ is context free$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
344
views
michael-sipser
theory-of-computation
context-free-language
regular-language
0
votes
0
answers
148
Michael Sipser Edition 3 Exercise 2 Question 19 (Page No. 156)
Let $CFG$ $G$ be the following grammar$.$ $S\rightarrow aSb \mid bY \mid Y a$ $Y\rightarrow bY \mid aY \mid \epsilon$ Give a simple description of $L(G)$ in English$.$ Use that description to give a $CFG$ for $\overline{L(G)},$ the complement of $L(G).$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
306
views
michael-sipser
theory-of-computation
context-free-grammar
context-free-language
1
vote
1
answer
149
Michael Sipser Edition 3 Exercise 2 Question 18 (Page No. 156)
Let $C$ be a context-free language and $R$ be a regular language$.$ Prove that the language $C\cap R$ is context-free. Let $A = \{w\mid w\in \{a, b, c\}^{*}$ $\text{and}$ $w$ $\text{contains equal numbers of}$ $a’s, b’s,$ $\text{and}$ $c’s\}.$ Use $\text{part (a)}$ to show that $A$ is not a CFL$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
335
views
michael-sipser
theory-of-computation
context-free-language
regular-language
0
votes
0
answers
150
Michael Sipser Edition 3 Exercise 2 Question 17 (Page No. 156)
Use the results of $\text{Question 16}$ to give another proof that every regular language is context free$,$ by showing how to convert a regular expression directly to an equivalent context-free grammar$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
294
views
michael-sipser
theory-of-computation
regular-language
context-free-language
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