Questions tagged [complexity-classes]

Questions about relationships between complexity classes.

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17 views

Does having a similar constraint while reducing a problem to similar problem to prove np hard means they are same?

I have been trying to find the computational complexity of my optimization problem and found that it is Np-Hard. To prove it to Np-Hard, I try reducing it Nurse Scheduling Problem. I am quite confused ...
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9 views

What is the complexity class of finding vertex cover number of a simple graph?

Suppose we have a simple graph $G$. We know that finding the minimum vertex covering set for $G$ is in the NP-hard class. But, what about the complexity class of finding the size of the set, i.e., the ...
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8 views

Is it possible to compute the minimum vertex covering set in quasi-polynomial time, by knowing the vertex cover number?

If we know the vertex cover number for a simple graph $G$ denoted by $\tau(G)$, is it possible to find the minimum vertex cover set for $G$‌ in quasi-polynomial time? As I found, we cannot find any ...
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23 views

On classes $\mathsf{\oplus PSPACE}$ and $\mathsf{\oplus L}$?

Savitch's theorem provides $\mathsf{PSPACE}=\mathsf{NPSPACE}$. Is there a class $\mathsf{\oplus PSPACE}$ analogous to $\mathsf{\oplus L}$ and is it known to be equal to $\mathsf{PSPACE}$? If $\...
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30 views

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 $\text{NTIME}(n^2) \subseteq \text{DTIME}(n^4) \Rightarrow \...
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43 views

Sufficient condition for a complexity class's closure under NP-reductions?

Let us say that there exists a $\mathsf{NP}$-reduction from a problem $A$ to another problem $B$ when there exists a non-deterministic, polynomial-time Turing machine $T$ such that for each $a \in A$, ...
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16 views

Is $E^{quasiP}$ equal $E$ or larger?

Let $quasiP$ be the quasipolynomial time complexity class. Is $E^{quasiP}=E$ false? Is $E^{DTIME(2^{(\log n)^k})}=E$ false at every $k>1$?
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30 views

Language in PSPACE that isn't PSPACE-hard and isn't in PH

Can there exist a language L in PSPACE such that L isn't PSPACE-hard and L isn't in the polynomial hierarchy (PH)? Intuitively, it seems like the answer is no, since TQBF is PSPACE-complete, and any ...
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108 views

What is the definition of Infinitely Often class in complexity

I was reading a paper and I came across the term $L\notin i.o.Dtime(2^{n^c}/n^c)$. What is the meaning of this?
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Naming of Monte Carlo and Las Vegas Complexity classes

For Curiosity Sake, I was wondering if there was some history behind the naming of "Las Vegas" and "Monte Carlo" classes. I've searched on the internet for quite some time now but ...
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39 views

What is the computational class of a pushdown automaton with real values?

Say there is a push-down automata, in this example I'll use a deadfish-like set: +: increase x by 1 0: set x to 0 ...
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46 views

Prove that $ln(n)^r \in o(n^p)$ for $p>0$ and $r\in \mathbb{R}$

I am trying to proof $f\in o(g)$ Let be $r,p\in \mathbb{R}$ with $p>0$ We have $f(n)=ln^r (n)$ and $g(n)=n^p$ I have already proofed that $ln(n)\in o(n)$ via l'Hospital $\lim\limits_{n\to \infty}\...
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29 views

Complexity class of problem whose running time features binomial coefficient

I've built an algorithm that, starting from an array of $n$ cells and an integer value $s$, builds $\binom{n+s-1}{s}$ vectors (that is, all the ways to add a certain $s$ quantity fully distributed ...
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116 views

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

For example, whether there exists $\mathsf{PSPACE}$-hard sparse language an open problem, as it is not yet known whether polynomial hierarchy collapses. But is it a solved problem for larger ...
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210 views

Why does SAT-UNSAT $\in NP \implies NP = coNP$

I was reading this post about the DP completeness of the problem SAT-UNSAT (both are well defined in this post). The answer added a note at the end that states the class complexity DP differs from NP, ...
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32 views

Is it a sufficient condition to be in NP?

Suppose the following situation. You have a decision problem $D$. You know that $SAT$ is $NP$-complete. You know that $D\leq_p SAT$. Can you conclude that $D\in NP$? I think it's true because it ...
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27 views

P vs NP characterization confusion

I know that $P \subseteq NP$, but for a problem in $P$, e.g. MST in a graph, is it a correct statement to say that: The MST problem belongs in NP-Class. (I mean, i think it is correct, but could ...
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55 views

Is there any consequence to the existence of $\mathsf{PSPACE}$-complete sparse language like with Mahaney's theorem?

Mahaney's theorem states that the existence of $\mathsf{NP}$-complete sparse language would lead to $\mathsf{P = NP}$. Is there any result result regarding the same for the complexity class $\mathsf{...
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193 views

Why don't passwords prove P != NP?

Pardon my ignorance on the matter but, Verifying passwords = Polynomial (linear) Guessing passwords = Exponential Since each guess has nothing to do with one another, exponential time is best possible ...
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54 views

What is the smallest time/space complexity class that is known to contain complxity class $\mathsf{SPARSE}$

Is it known if complexity class of all sparse languages is contained within e.g. $\mathsf{EXP}$ or $\mathsf{EXPSPACE}$? Or what is the smallest time or space complexity class that contains complexity ...
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364 views

Are there any known W[3] or W[3]-hard problems?

We are currently working on a variant of domination parameter and we have shown that it is in W[3] with regard to parameterized complexity. To show it is W[3]-complete, we must show the problem is W[3]...
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Is QMA known to contain Co-NP?

Is QMA known to contain Co-NP? If not, would Co-NP being contained in QMA have any implications for other complexity classes. (e.g. Causing the polynomial heirachy to collapse.)
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85 views

Conway's Game of Life: Is it really P-complete?

Wikipedia claims that the Game of Life is P-complete (or the decision problem version of it is; the function version, I suppose, would then be FP-complete). Colloquially, P-complete and FP-complete ...
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75 views

Nondeterministic polynomial time algorithm versus certificate/verifier for showing membership in NP

In this paper (https://arxiv.org/pdf/1706.06708.pdf) the authors prove that optimally solving the $n\times n\times n$ Rubik's Cube is an NP-complete problem. In the process, they must show that the ...
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67 views

If X is polynomial-time reducible to Y and X is polynomial-time reducible to Z then Y is polynomial-time reducible to Z?

If $X$ is polynomial-time reducible to $Y$ and $X$ is polynomial-time reducible to $Z$, $Y$ is polynomial-time reducible to $Z$? If $X \leq_p Y$ and $X \leq_p Z$ then $Y \leq_p Z$? True, false or we ...
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79 views

If X is in NP then $\overline{X}$ is in NP. True, false or “we don't know”? Why?

If X is in NP then $\overline{X}$ is in NP. True, false or "we don't know"? Why?
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If X is polynomial reduction to Y and Y is in NP, then X is in NP? [duplicate]

If X is polynomial reduction to Y and Y is in NP, then X is in NP? Is this true, false or "we don't know"? Why?
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48 views

Complexity of approximating a function value using queries

I am looking for information on problems of the following kind. There is a function $f: [0,1] \to \mathbb{R}$ that is continuous and monotonically-increasing, with $f(0)<0$ and $f(1)>0$. You ...
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1answer
47 views

Complexity of generating power sets

Suppose I have two sets $A$ and $B$ containing integers. Let $B'$ be the power set of $B$. Then suppose I have an algorithm that enumerates all possible pairings of elements in $A$ and $B'$ to apply a ...
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36 views

A question regarding definition of Deterministic Subexponential Time (SUBEXP)

First Look at the definition of SUBEXP from Complexity Zoo: SUBEXP: (Deterministic Subexponential-Time) The intersection of DTIME($2^{n^\epsilon}$) over all $\epsilon$>0. (Note that the algorithm ...
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61 views

Arthur-Merlin protocol

I recently learned about the Arthur-Merlin protocol, and we defined the complexity classes $AM,MA$. We have also seen that there exists a theorem stating that $AMAMAM...AM=AM$, however we have not ...
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65 views

Is finding solution to a system of 2SAT equations seperated by OR (DNF form) in NP

I want to know if finding solution to a specific number of 2SAT equations sepearted by OR gate (DNF form as below) is in P or NP. The equation has total n variables and each clause is a 2SAT equation ...
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If $PSPACE^{SAT}=PSPACE$ and $PSPACE \subseteq EXP$, then why does $EXP^{SAT}$ not necessarily equal to $EXP$?

I read the following claim: $PSPACE^{SAT}=PSPACE$ $EXP^{SAT}$ is not necessarily the same as $EXP$ The first claim makes sense; $PSPACE \subseteq PSPACE^{SAT}$ trivially, and for any language $B \in ...
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37 views

why is $\Pi_2$ smaller than $NP\cap coNP$

Consider the language $A=\{(\phi_1, \phi_2) | \phi_1 \in SAT, \phi_2\in \overline{SAT} \}$. What is the smallest class that $A$ is known to belong to? Apparently, the answer is $\Pi_2$, although I ...
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25 views

If $NTime(2^n) \subseteq DTime(n^n) $, then what can you conclude about $DSpace(n^n)$?

Assume $NTime(2^n)\subseteq DTime(n^n)$, what can you conclude about $DSpace(n^n)$? I don't know if this is the correct approach, but here was my attempt at an answer: Let $A \in DSpace(n^n) $ and ...
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33 views

Complexity of class finding selection of entries in matrix

Suppose I have a matrix with entries either $x$ or $y$, where the number of rows = number of columns = $n$. If I want to select/circle $n$ entries such that for each row, only exactly one is circled, ...
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Can you give an example of a problem in $EXP^{RE}$ but not In $P^{RE}$

Can you give an example of a problem in $EXP^{RE}$ but not In $P^{RE}$?
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56 views

Problem with proving that $RP \subseteq NP$ : a non-deterministic TM for a language $L \in RP$

I'm having a small issue with wikipedia's proof that $RP \subseteq NP$: An alternative characterization of RP that is sometimes easier to use is the set of problems recognizable by nondeterministic ...
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Are there any “natural problems” which are known to be NPI under weak assumptions

Are there any "natural problems" which are known to be NPI under weak assumptions. By weak assumptions I mean something like $P \neq NP$ or $NP \neq Co-NP$
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What is $S2-EXP•P^{NP}$?

What is $S2-EXP•P^{NP}$? I saw in on the complexity zoo site without any explanation of what it is. Coul someone please explain it?
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53 views

Proof that if P=PSPACE, RP=BPP

Like the title says. I can't figure out how to prove this. I think it probably has to do with the polynomial hierarchy collapsing but I'm not sure.
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78 views

Is the BPP class closed for union and intersection?

Just like the title says. I want to prove that given two languages $L_1,L_2 \in BPP$, $L_1 \cup L_2 \in BPP$ and $L_1 \cap L_2 \in BPP$
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48 views

What is and amplification factor in pseudo-random generators?

I can't seem to find an answer to this. For instance, I have this question: Show that, if $P=NP$, there aren't any pseudo-random generators (even with amplification factor $n+1$). My gut tells me this ...
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Is this Correct, the existence of cryptography requires $UP \cap Co-UP \not\subseteq BPP$

Is this Correct, the existence of cryptography requires $UP \cap Co-UP \not\subseteq BPP$? Or does it require $UP \not\subseteq BPP$?
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What complexity class results would be implied by a proof of the existence of one way functions

What complexity class results would be implied by a proof of the existence of one way functions. (Apart from the obvious $P \neq NP$) I thik it would imply $P \neq UP$, but what else?
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91 views

What complexity class is the TSP problem?

Is the travelling salesman problem (TSP) $FNP$-complete or is it $FP^{NP}$-complete?
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Is $NC_1$ vs PP still an open problem?

Is $NC_1$ vs PP still an open problem? I done a few searched but I can't find an answer.
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25 views

Assuming the Exponential Time Hypothesis is true, what's the fastest possible algorithm that can be produced for NP-complete problems? [duplicate]

Assuming the Exponential time hypothesis is true, what's the fast possible algorithm that can be produced for NP-complete problems? If 3-Sat takes exponential time, then could it be possible that ...
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19 views

What decision problems are their that are outside of elementary but still decidable

What decision problems are their that are outside of ELEMENTARY but still decidable? I'm curious about problems that are still solveable, but take a very long time to do so.
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124 views

What's the complexity class of determing the halting problem of a finite memory Turing machine?

What's the complexity class of determining the halting problem of a finite memory Turing machine? What is the computational complexity class of determining whether a machine halts on any input if it ...

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