Questions tagged [complexity-classes]

Questions about relationships between complexity classes.

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21 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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2answers
29 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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0answers
24 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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0answers
48 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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1answer
79 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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1answer
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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1answer
26 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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1answer
51 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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3answers
171 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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2answers
50 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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1answer
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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1answer
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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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1answer
53 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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1answer
43 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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1answer
35 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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1answer
41 views

If X is polynomial reduction to Y and Y is in NP, then X is in NP?

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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0answers
45 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
24 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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1answer
32 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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1answer
39 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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1answer
53 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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1answer
29 views

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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1answer
33 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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0answers
21 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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1answer
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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14 views

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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1answer
39 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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0answers
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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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9 views

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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1answer
45 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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1answer
45 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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1answer
47 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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19 views

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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41 views

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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1answer
75 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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25 views

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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22 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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0answers
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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1answer
67 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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1answer
115 views

Is P/poly known to be in RE?

Is P/poly known to be in RE? If yes what other classes is it known to be part of.
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26 views

What's the class of problems solvable in polynomial time with an exponential number of processors?

What's the class of problems solvable in polynomial time with an exponential number of processors? I am asking this because I'm curious about the class of problems that could feasable be solved on a ...
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20 views

What would the conqesquences of finding a quasi polynomial-time algorithm for 3-Sat?

What would the conqesquences of finding a quasi polynomial-time algorithm for 3-Sat? Would this result in their being a quasi polynomial-time algorithm for all NP-complete problems?
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43 views

What are the $EXP^{NP}$, $EXP^{PSPACE}$, and $EXP^{EXP}$ equal to

What are the $EXP^{NP}$, $EXP^{PSPACE}$, and $EXP^{EXP}$ equal to? I suspect that their, NEXP, ESPACE and 2EXPtime respecitvely. And what bout $NP^{EXP}$
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31 views

Are there problems that are known to be in ZPP but not in p

Are there any problems that are known to be in ZPP but not in p?
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78 views

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.
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1answer
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Close To Cook Reduction given NP != coNP

I am struggling to answer these two questions: Prove or wrong: Both are given the assumption that NP != coNP. For any 2 decision problems S, S', if there is a Cook reduction from S' to S then there ...
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1answer
86 views

Is every linear language in NL?

I wonder if all the linear languages are in NL? I was thinking that we can take an input-language $L$ and convert it to linear normal form. If this is not possible, the machine rejects. If the ...
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0answers
65 views

What about problems that are fixed parameter tractable with an algorithm that does not inspect the parameter?

A parameterized problem is a subset $L \subseteq \Sigma^* \times \mathbb N$, where $\Sigma$ is a finite alphabet. A parameterized problem is fixed parameter tractable, if it could be decided in time $...
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1answer
43 views

$\text{DSPACE}(O(1))=\text{REG}$ Proof?

I want to know why $\text{DSPACE}(O(1))=\text{REG}$, especially in the direction of why all languages in $\text{DSPACE}(O(1))$ can be recognized by a finite automaton. I've thought for some time and ...

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