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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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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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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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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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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 ...