Linked Questions

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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 ...
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0answers
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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 ...
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0answers
64 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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0answers
41 views

Language involving length constraints and reversal

Why is the language $A=\{wtw^r: w,t\in\{0,1\}^*\text{ and }|w|=|t|\}$ not a context free language? It is turning out to be really tricky. Is there an easy way to show this?
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1answer
163 views

Prove that this language is not context-free [duplicate]

I'm not very comfortable with pumping lemma for context-free grammar. I understand the sufficient conditions that must hold but proving it gets me everytime. For example, I need to prove whether $L=\{...
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0answers
5k views

Context Free Grammar for $\{A^nB^nC^n | n \in \mathbb{N}\}$ [duplicate]

Is $L = \{A^n B^n C^n \mid n \in \mathbb{N}\}$ a context-free language, e.g. $AAAABBBBCCCC \in L$ If so, what's that context-free grammar that produces it?
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1answer
157 views

Is $\{u u^R u : u \in \Sigma^*\}$ context-free?

Given a finite alphabet $\Sigma$ with more than one symbol, is $L = \{u u^R u : u \in \Sigma^*\}$ context-free? ($u^R$ is the reverse word of $u$) I tried to show it wasn't context-free by using the ...
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1answer
1k views

PDA or CFG for language $L= \{a^ib^j | 2i \leq 2j \leq 3i, i>0\}$

Can someone help with this $L= \{a^ib^j | 2i \leq 2j \leq 3i, i>0\}$
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1answer
134 views

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

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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1answer
197 views

Is the language $L=\{a^nb^m \mid n>2^m\}$ context-free?

I cannot go on with this exercise: Determine whether $L = \{a^nb^m \mid n > 2^m \}$ is context-free. Let's suppose that $L$ is context-free. According to the pumping lemma, there exists $N > ...
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1answer
186 views

Push-down Automata Construction

Construct a push-down automata to recognize the language $ A = \{u\#v \in \{0,1,\#\}^{*} | u = v^{\complement} \} $. Here, $v^{\complement}$ is the bit-complement of v. I don't see how to perform ...
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1answer
236 views

Proving the language of words with equal numbers of symbols non-context-free [duplicate]

Possible Duplicate: How to prove that a language is not context-free? I'm having a hard time figuring this out, any help is appreciated. Let EQUAL be the language of all words over $\Sigma = \{...
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1answer
127 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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1answer
428 views

Prove that $L = \{ a^ib^jc^k | i < j \ and \ i+2j +3 < k \}$ is not CFG

Can someone help me prove that $L = \{ a^ib^jc^k | i < j \ and \ i+2j+3 < k \}$ is not a context free language? I've tried applying the pumping lemma for CFGs and proving case by case (taking ...
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1answer
112 views

Show Language is not context free without pumping lemma [duplicate]

Can we show that following language is not context free using Push down automata approach? L = {a^i b^i a^i : i>=1} For every a we will Push 'A' onto stack, ...

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