complexity-classes

Which is harder, an NP-complete problem or the Raz-Tal oracle problem?

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This is a (hopefully) sharper version of a question that I asked previously. Which of these algorithms is believed to have a longer asymptotic runtime? The optimal algorithm guaranteed to solve some NP-complete problem using a standard Turing machine. The optimal algorithm guaranteed to solve the problem described by Raz and Tal using a Turing … Read more

What are some of the most ridiculous claims in computer science that we haven’t disproved?

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What are some of the most ridiculous possible claims in computer science that we haven’t disproved? E.g. For example the claim that ZPP=exptime is absurd but has not been disproven. Answer AttributionSource : Link , Question Author : blademan9999 , Answer Author : Community

What is the smallest time/space complexity class for which no sparse language is hard?

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For example, whether there exists PSPACE-hard sparse language an open problem, as it is not yet known whether polynomial hierarchy collapses. But is it a solved problem for larger complexity classes like EXP or PR? What is the smallest complexity class (that is larger than PSPACE) for which it is a solved problem? Answer AttributionSource … Read more

An opposite method of padding argument on N/DTIME complexity class

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Is there a method to prove things with longer input in complexity theory? For example, using padding argument it’s trivial to show that NTIME(n2)⊆DTIME(n4)⇒∀k≥2,NTIME(nk)⊆DTIME(n2k) Is there a common method for the opposite direction, i.e., for something like NTIME(n4)⊆DTIME(n12)⇒∀1≥k<4,NTIME(nk)⇒DTIME(n3k)? Answer AttributionSource : Link , Question Author : homecute , Answer Author : Community

Consequence of NP-complete, and DP-complete w.r.t. randomized reductions

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If a problem is NP-complete with respect to randomized (polynomial time) reductions, but not with respect to deterministic reductions, then we have P ≠ BPP (See Question 2 here and its answer). Suppose a decision problem is proved to be NP-complete; and it is also proved to be DP-complete with respect to randomized reductions. Does … Read more

WW-hierarchy and parameterized search problems

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I have two related questions: What are the ways to prove that a certain problem is in W[t] in the W-hierarchy for parametrized complexity, except using the straight definition of boolean circuits? I mean, is there a similar classification like for the FPT class, that if there exists an algorithm which runs in a certain … Read more