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what is the complexity of $FP^{NP}$ w.r.t. $FPSPACE$? Also can someone please provide a few examples of Problems complete for $FP^{NP}$? If possible let the examples be natural.

The decision version of $TSP$ is $NPComplete$. I was reading about the functional version of $TSP$ i.e. the class $FP^{SAT}$. It is mentioned in the original paper that TSP is complete for the class …

I an trying to learn about $DisNP$ Complexity class. I couldn't find this class in any book. But, regarding it, I found this definition in a paper: Definition: A disjoint NP-pair (NP-pair for short) …

According to wikipedia (https://en.wikipedia.org/wiki/P-complete): The most basic P-complete problem is this: given a Turing machine, an input for that machine, and a number T (written in unary), do …

I know that monotone 3SAT is NPComplete. Also, 1 in 3SAT is NPComplete. I think both conditions together also leave the problem NP Complete (need confirmation). If possible can someone please help w …

Given: 3 positive integers $a,b,L$. Problem: Is there a positive integer $x<L$ such that $x^2≡ a(mod\ b)$? The above problem is NPComplete (as mentioned in G&J) even if we have the factorization of $ …

I was going thorough this paper: (P=BPP unless E has sub-exponential circuits: https://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/IW97/proc.pdf) and I am somewhat struggling with some basics from the …

Given that both $P \subset \mathit{NP}\ ?$ and $P^{\mathit{NP}} \subset \mathit{NP}^{\mathit{NP}}\ ?$ are open questions. Is it possible that $P \subset \mathit{NP}$ and $P^{\mathit{NP}} =\mathit{NP}^ …

Assuming (the unlikely scenario) that the Polynomial Hierarchy collapses to second level. Thus, $\Sigma_2^p=PSPACE$. How significant this result would be (broad consensus) as compared to the other ope …

Given two unrelated languages $L_0$ and $L_1$ contained in some complexity class $C$. Is the language $L_x=L_0\times L_1= \{(x,y)|x\in L_0, y\in L_1\}$ always contained in $C$? And if that is the case …

Given a 4SAT instance such that: Each clause has 2 negative and 2 positive literals. Thus, the clause is 'balanced'. Each literal occurs exactly 2 times. Is this instance of 4SAT NP-complete? I am a …

Given a 3-SAT instance. How do we convert it into: 1 in 4 SAT instance. 2 in 4 SAT instance. each case minimizing the [number of new variables - number of new clauses] difference? Note: We are not ad …

I am aware of the complexity classes $P$, $NP$ and $L$. But I am not clear what $NL$ or Non-deterministic Log Space intuitively means. The part what I am unclear about is what is the meaning of Non-de …

I am trying to understand two player (prover-Merlin and verifier-Arthur) interactive proof complexity classes and had a few doubts. As I understand, the classes $MA$ and $AM$ involve two players, wher …

Considering the complexity classes $NP$, $co-NP$ and $PP$: $NP$ and $co-NP$ are both contained in $PP$. For any Language $L$ suppose we have the mechanism that: If the oracle of $co-NP$ implies $No$ …