Tagged Questions

Questions about operations on objects of some kind that result in objects of the same kind.

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Is intersection of regular language and context free language is “always” context free language

I have read that intersection of regular language and context-free language is always context-free. Most of the places an standard example has been used to prove this, e.g., \begin{align*} L_1 &= ...
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proving that pp closed under cook reductions [closed]

I tried to prove or disprove that pp is closed under cook reductions. anyone has a idea or link to a answer?
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when can I know if a class (complexity) is closed under reduction (cook/karp)

How do I know if a class let's say PP , is closed under cook reduction or not closed? I understand the concept of reduction (how to use it mainly) , but still can't figure out the meaning behind it, ...
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Proving that PP is closed under symmetric difference

I want to prove that PP is under symmertic difference. let A be a language in PP and B likewise. I tried showing that : (A\B) U (B\A) in PP , so by show each in PP and then showing that it's closed ...
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Turing Machine and decidability

so the thing is that i have to prove that if the language $L ⊆ \Sigma^*$ is decidable then both languages are also decidable. $$P_1(L) = \{w ∈ Σ\mid \text{ For every prefix v of w, we have }v ∈ L\},$$ ...
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How to Trace Path in Proof that Regular Languages are Closed Under Reversal

I'm self studying automata theory and I need help with proving that regular languages are closed under reversal. I have a basic proof, but am unsure about last statement in my proof. Is this ...
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Show that P is closed against the Kleene star

I have that question that looks kinda easy at first but it is quit hard. Let $L\in P$. Prove that $L^*\in P$ my approach: I tried to generate a turing machine but I got stuck with the thing of ...
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Why DCFL is not closed under kleene star?

I have read somewhere that DCFL is not closed under kleene star. but I haven't found any example
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Is NEXP = co-NEXP?

It is known that $\mathsf{NL}=\mathsf{Co{-}NL}$ and unknown if $\mathsf{NP}=\mathsf{Co{-}NP}$. But what about $$\mathsf{NEXP}=\mathsf{Co{-}NEXP}?$$ Is it known whether these two classes are equal?
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Finding the mistake(s) within this “proof” of NP being closed for complement

For my classes in theoretical computer science the following proof must be shown to be wrong. However, this is the first time I am attempting myself at this topic, so I would be thankful for some help:...
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Why do we study closure properties of formal languages?

In automata theory we study formal languages like Regular, CF, CS and etc. and each of them have their own closure properties under union, intersection, star and etc. . I like to know, why it is ...
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Closure properties of the class of inherently ambiguous CFLs

is set of inherently ambiguous context free languages close under operations such that union, intersection, kleene star, concatenation, reverse, complementation and etc. how many of theme are answered?...
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Why are palindrome and not-palindrome both context-free?

Both palindrome and its complement are context-free. This is very interesting. Both are non-deterministic context-free, which in general are not closed under complement. What is it about these two ...
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If L is a regular language then the language replace(L,σ,τ) is also regular

I am stuck at the following problem: Prove that if $L$ is a regular language over some alphabet $\Sigma$ and that $\sigma, \tau \in \Sigma$, Then the language $replace(L,\sigma,\tau)$ is regular. ...
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If a language is X-complete, is its complement is X-complete as well?

I'm looking for an information about closure of complexity complete classes. Is it true that any language, if the language is X-complete, then its complement is X-complete? Why? I was thinking ...
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How to prove that the decidable languages are closed against iteration only by enumerators?

We have the $L\in R$, how can we prove that $L^*\in R$ only by enumerators? I try to use induction, but as I understand I wrong... I'd like to get any help!
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Closure under reversal of regular languages: Proof using Automata

I have been studying the closure properties of regular languages, referencing the book Introduction to Automata Theory, Languages, and Computation by John E. Hopcroft and Jeffery D. Ullman. Under the ...
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Want to show that if P = NP, then P = NP = CoNP [duplicate]

I want to show that if P = NP, then P = NP = CoNP. Essentially, I want to show that if the set of problems which can be solved in polynomial time is exactly the set of problems which can be checked in ...