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

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?

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?

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

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

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

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