Questions tagged [complexity-classes]
Questions about relationships between complexity classes.
413
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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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1answer
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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1answer
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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0answers
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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0answers
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 \...
3
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0answers
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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1answer
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 $k>1$?
2
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0answers
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 ...
2
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1answer
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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12 views
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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1answer
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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2answers
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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0answers
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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1answer
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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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
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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1answer
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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3answers
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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2answers
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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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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0answers
18 views
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.)
5
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1answer
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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1answer
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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0answers
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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2answers
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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1answer
81 views
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?
2
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0answers
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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1answer
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 ...
1
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1answer
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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1answer
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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1answer
30 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
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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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
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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0answers
17 views
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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10 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
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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1answer
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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1answer
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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0answers
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
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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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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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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1answer
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 ...
