Linked Questions

0 votes
1 answer
89 views

Proof that $\{a^ib^jc^k\mid i,j,k\in\mathbb{N}, i<k<j\}$ is not context-free using the Pumping Lemma

$$ L=\{a^ib^jc^k \;| \;i, j, k \in \mathbb{N} \; \text{and} \; i <k<j\} $$ I need to show that this language is not context-free with the help of the Pumping Lemma. My first intuition is, that ...
  • 1
15 votes
2 answers
717 views

Is the language of words that are unbalanced in the first half context-free?

(Practice exam question in computational models) Definition: A word $w\in \{0,1\}^*$ is called balanced if it contains the same number of $0$s as $1$s. Let $L = \{w\in \{0,1\}^*\mid |w|$ is even and ...
1 vote
2 answers
546 views

Is a^mb^n where m=n^2 a CFL?

Is $a^mb^n$ where $m=n^2$ a CFL? I have a doubt regrading this problem. Say if we pop $n$ number of $a's$ from the stack for each $b$ then it is a CFL (to be exact DCFL) right? On the other hand I ...
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0 votes
1 answer
258 views

$L = \{ a^{j!} \mid j \geq1\}$ is not context free by pumping lemma

How I use the pumping lemma to prove that the language $L = \{ a^{j!} \mid j \geq1\}$ is not context-free?
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1 vote
1 answer
122 views

Acceptance problem for CFGs is not regular

Let $ACFG$ be the language of all encodings $(C,x)$ where $C$ is a context-free grammar that generates a language containing $x$, i.e. $ACFG$ is the acceptance problem for context-free grammars. It is ...
-1 votes
1 answer
26 views

Is there any tiny tips to find counter example string for proving some language is not a CFL? [duplicate]

When I prove some language is context free, It is too hard to find example string. Is there any tips? It takes too many time or eventually give up.
1 vote
1 answer
44 views

How to prove that a language is not context-free using pumping lemma

I'm trying to prove that that language isn't a context free: $ L = \{ w11w \mid w\in \Sigma^* = \{0,1\}\}$ I succeed to prove that $L = ww$ isn't context free, but not the language above. What ...
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0 votes
0 answers
21 views

How to prove this language is not context-free language by pumping lemma? [duplicate]

Could I get help to prove that the language $\{a^i b^j c^k \mid i>j>k\ge 0\}$ is not context free language by using pumping lemma?
1 vote
1 answer
113 views

Is this language is Context-free language or not?

Is anybody can help me please to determine is this language is Context-free language or not? L={wvw | w,v∈{a,b,c}+} for example: part of the language: acbac, abcab, bbcbb not part of the language:...
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1 vote
0 answers
12 views

Context free/Non Context free Language [duplicate]

Let L = { uv composed of {0,1} | |u| = |v| and u = v } Do we agree that this language is not a Context Free Language ? If not, why ? Can you give me a pushdown automata that recognizes it or the ...
3 votes
2 answers
198 views

Can the pumping lemma for context free languages be extended to any subword?

It is known that in the case of a Regular Language $L$ , the pumping lemma can be extended to apply to any sufficiently long subword of the language, ie, if $uwv \in L$ and $|w| \ge p$ then we can ...
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-1 votes
1 answer
71 views

How construct PDA to $L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$

$L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$ I don't have any idea. Can someone help me.
0 votes
1 answer
487 views

Prove $ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ is regular or context-free or neither

$ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ Exercises: If the language L is regular (build a DFA or regular expression) else if the language L is context-...
0 votes
0 answers
155 views

Is this language context-free? $\Sigma$ = {a,b,#} L = {x1#x2#...#xk : k$\geq$2, every $x_i \in$ {a,b}* and xi $\neq$ xj for every pair i $\neq$ j} [duplicate]

Is this language context-free? $\Sigma$ = {a,b,#}, L = {x1#x2#...#xk : k$\geq$2, every $x_i \in$ {a,b}* and xi $\neq$ xj for every pair i $\neq$ j} I think it is not, because the PDA can't memorize ...
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0 votes
1 answer
125 views

Prove or disprove if L is CFL? [duplicate]

Given $L=\{a^ib^jc^k | i\neq j \space and \space j=k\}$. Is this CFL? How do I write CFG for it or prove it with pumping lemma? Thanks.
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1 vote
0 answers
208 views

Is $\{a^mb^nc^{mn}\mid m>n\}$ a context-free language? [duplicate]

Been trying to figure it out for an hour myself and another hour looking around, I cannot find anything with the $c^{mn}$ part. $$L=\{a^mb^nc^{mn}\mid m>n\}$$
0 votes
1 answer
199 views

Does a pushdown automata exists for the following language?

I have came across a question stating that language $L = a^n b^n c^{2n}$ is not a context free language and hence, no PDA can be constructed for it. But what I am wondering is that, if I add another ...
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2 votes
1 answer
2k views

How to prove that $L = \{a^n b^m a^n b^m \mid n,m \ge 0\}$ is not a CFL?

I'm stuck with the proof. I've tried Ogden's lemma but it doesn't seem to help. The problem is: Let $N$ be the constant of Ogden, let $z = a^N b^{N+1} a^N b^{N+1}$, and $z = uvwxy$. Now I should ...
0 votes
0 answers
15 views

Non-context free languages with word degree [duplicate]

I have stumbled across these 2 problems $L_1= \{\alpha \mid w \in \{a,b\}^* | \alpha $ has exactly 2 b's$\} $ ,prove that $L =\{ \alpha^n | \alpha ∈ L_1 ,n \ge 0 \}$ is not context free Given : $...
  • 1
0 votes
0 answers
16 views

How do we determine p (pumping length) in pumping lemma for CFL? [duplicate]

This has been confusing me for a while, how do we exactly choose the pumping length when we want to prove whether a language is CFL or not. For example, when we want to prove that {ww, w: {0,1}* } why ...
0 votes
1 answer
426 views

Pushdown Automaton for $L = \{ w_1 w_2 : |w_1| =|w_2| , w_1 \neq w_2 \} $ [duplicate]

So i know that $L =$ { $ {w_1 w_2 : |w_1| =|w_2| , w_1 \neq w_2} $ } is a CFL, but i cannot make a PDA for it because it doesn't make any sense to me why this is CFL i even know the grammar for it ...
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1 vote
0 answers
91 views

Proof that the language is not regular (Pumping Lemma) [closed]

I have to prove that the following language is not regular: $$\{ x | x = 10^{2n} + 10^n + 1, n ≥ 1\}$$ I am trying to prove it using Pumping Lemma, however, when I expand the expression I have both ...
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0 votes
0 answers
13 views

Choose a specific regular language to prove a language is not regular [duplicate]

I've tried a few tricky languages such as D = { w | w has an equal number of occurences of 01 and 10 as substrings} but I don't have the means to prove this one as being not regular (and I cannot ...
0 votes
1 answer
42 views

Is the language $L = \{a^pb^q \ | \ p \ge 1, \ q \ge 1, \ p \ge q^2 \ or \ q \ge p^2\}$ context free? [duplicate]

Is the language $L = \{a^pb^q \ | \ p \ge 1, \ q \ge 1, \ p \ge q^2 \ or \ q \ge p^2\}$ context free? I should probably use Ogden's lemma, but I don't know how to do that in this case.
0 votes
1 answer
86 views

Using closure properties to show that $L_1=\{a^lb^mc^m|l,m\ge 0\} \cup L(b^*c^*)$ is regular or not

i'm trying to figure out whether this Union $\left [ L_1=\{a^lb^mc^m|l,m\ge 0\} \cup L(b^*c^*)\right]=K$ is regular or not, now since regular languages are closed under intersection, so i assume $K$ ...
0 votes
1 answer
211 views

Pumping lemma to show a language is not context free [duplicate]

I have started pumping lemma for context-free grammar by reading Sipser's book and there are two questions right at the end end of the topic which I don't understand how to solve or where to start ...
  • 153
0 votes
1 answer
373 views

Pumping lemma with multiple of prime number + a constant

Given the language $$L = \big\{ 0^{m} 1 0^{2m+k} \mid m \text{ prime and } k \ge 1 \big\} $$ show that $L$ is not context free by giving a counterexample of the context free pumping lemma. It may be ...
  • 549
0 votes
1 answer
40 views

Is the language in the description context free? [closed]

I am stuck on a question. Lets say there is a string that can be created from three alphabets a,b,c the condition is number of a<= number of b<= number of c. I can solve if there are a and b (...
0 votes
0 answers
212 views

How to show that a language is strictly context sensitive

During a class, we was asked how to prove that a language L is strictly context-sensitive. In particular, we have to prove that $L = \{a^nb^nc^n \mid n > 0\}$ Could you help me to find the ...
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0 votes
0 answers
157 views

A push down automaton that recognize exponential strings

How can I describe a Push Down Automaton that recognize the language $P=\{a^{2^n} | n \geq 0 \}$? My approach I know that the language can be described by a Turing Machine, but how i can the stack ...
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