Questions tagged [p-vs-np]
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P vs. NP and Godel's Theorems
This post is based loosely on a previous post, but the presentation is somewhat different and hopefully much more succinct.
Basically, I'm wondering if it is plausible for there to be a formal proof ...
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1answer
84 views
P vs NP question from GeeksforGeeks
From here: https://www.geeksforgeeks.org/algorithms-np-complete-question-2/
Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to ...
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1answer
61 views
What's the flaw in the P != NP proof in the article “The Computational Complexity of the Traveling Salesman Problem”
I am reading through some proof of inequality of P and NP
but they are not accompanied by the flaws in the reasoning so I'm trying to find them by myself, just to see if I'm getting the logic right. ...
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Contradiction proof for inequality of P and NP?
I'm trying to argue that N is not equal NP using hierarchy theorems. This is my argument, but when I showed it to our teacher and after deduction, he said that this is problematic where I can't find a ...
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1answer
80 views
A tricky P=NP problem
Define an operator $\pi(\cdot)$: for a language $L$, $\pi (L)$ is the set of all prefixes of strings in $L$ with length at least half of the original string. Prove that if $\mathsf{P}$ is closed under ...
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26 views
Reducing SAT to a P problem in polinomial time [duplicate]
Does reducing SAT in polynomial time to a P problem would mean that P = NP?
2
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1answer
53 views
What is Ironic complexity? What are some good resources to learn about it?
The term "Ironic complexity" was coined by Scott Aaronson for the stuff Ryan Williams does in the area of complexity theory. Could anyone tell me what kind of problems and approaches does Ryan ...
5
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1answer
2k views
If graph isomorphism is in P, is then P = NP?
I think that, since graph isomorphism is not known to be $\textbf{NP}$-complete, we can not reduce all problems in $\textbf{NP}$ to it, and therefore the implication does not hold.
Additionally, in ...
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1answer
34 views
Effective Procedures and P vs NP Problem
If, suppose, P doesn't equal NP. Implication of this statement is that there is no effective procedure to solve a hard problem; however there exists an acceptable solution S. I have following two ...
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1answer
114 views
Why any problem can be reduced to SAT is NP-Complete?
I have a book statement says the title, I don't understand it. From my current understanding if a problem A can be reduced to a problem B then it only means B is at least as difficult as A.
3
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66 views
Given that A reduces to B in $O(n^2)$ and B is solvable in $O(n^3)$, solve A
Suppose a problem A reduce to problem B and reduction is done in $O(n^2)$ time.
If problem B is solved in $O(n^3)$ time then what about the time complexity of problem A?
Approach:
A is reduced ...
0
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1answer
49 views
Can we detect perfect matchings in P? in NP? in coNP?
This question concerns the classes P and N P . If you are familiar with them, you may skip the definitions and go directly to the question.
Let L be a set. We say that L is in P if there is some ...
2
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1answer
67 views
Are there problems that are DSPACE(O(1)) complete?
I know there are problems that are NL-complete, NP-Complete, PSPACE-complete, etc. Are there problems that are DSPACE(O(1))-complete I.e. NSPACE(O(1))-Complete I.e. Reg-Complete?
Thanks!
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0answers
58 views
What can be a Zero Knowledge Proof of a working SAT Algorithm?
Me and my colleague are exploring new ideas to solve SAT efficiently (i.e. in polynomial time) and it's the case that there is a candidate algorithm.
Unfortunately, neither of us can write scripts ...
0
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1answer
62 views
Does indirect diagonalization a relativize technique?
My main question is can with R.kanon , Fortnow ,... technique that shows lower bounds for SAT seperate P and NP ?
Baker-Gill-Solovay showed that $P?=NP$ could not be solved with relativization. Does ...
3
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1answer
311 views
Chomsky Hierarchy and P vs NP
I have read multiple questions here that involve this kind of subject but I haven't found any definite answer. In what class do regular languages belong? (P or NP or some regular are P and other NP), ...
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1answer
63 views
Are there infinite possibilities to the outcome of the P vs. NP question?
The P vs. NP poll provides 3 possibilities: equal, not equal, and independent. This is reasonable, because despite the law of the excluded middle you must supply a proof for your answer, which itself ...
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1answer
35 views
What's wrong with the following argument that $NP \subset coNP$? [duplicate]
What's wrong with the following argument that $NP \subset coNP$?
let $L \in NP$; then there exists an NTM $N$ that decides $L$ in $f(n)$ time where $f(n) = O(n^k)$ for some natural number $k$.
...
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2answers
181 views
Does Provable P equal Provable NP?
My question is a very basic one. It seems feasible to believe that $\mathsf{P = NP}$, because there is some "pathological" good algorithm for SAT, yet it is impossible to prove that the algorithm is ...
1
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1answer
269 views
P vs NP problem (Student example)
Hello dear stackexchangers,
I have a simple question, and I would like to say that I am not a scientist. When I read the problem statement on this link: http://www.claymath.org/millennium-problems/p-...
4
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1answer
168 views
Logical characterization of P versus NP problem (and references for least fixed point logic)
Wikipedia says the following (and more) about the logical characterization of the P versus NP problem here:
Thus, the question "is P a proper subset of NP" can be reformulated as "is existential ...
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2answers
368 views
P vs NP and can an oracle make P=EXPTIME?
As I understand, diagonalization cannot be used to prove or disprove P vs NP, because for some oracle $A$, $P^A = NP^A$, whereas under another oracle $B$, $P^B \neq NP^B$.
I don't fully understand ...
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1answer
48 views
Independence Implies P $\ne$ NP
Suppose P vs. NP is independent of ZFC. Then there cannot be an efficient SAT solver, otherwise it would constitute a proof for P = NP. Therefore P $\ne$ NP.
What we see here is that independence ...
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733 views
Why doesn't Godel's Second Incompleteness Theorem rule out a formalizable proof of P!=NP?
I'm sure there must be something wrong with the following reasoning because otherwise a lot of P vs. NP research would be curtailed but I cannot determine my error:
For any fixed integer $k>0$ ...
3
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2answers
110 views
How are boolean circuits used for solving P vs NP?
In the paper https://web.stanford.edu/~gavish/documents/sipser-pvsnp.pdf , it is mentioned under the Status section that boolean circuits have been used to try and solve P vs NP. Can anyone explain to ...
2
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2answers
159 views
Is every problem in NP?
My friend and I were studying NP-hard problems and NP-completeness. I don't think we have understood the concept very well so I thought I would come here to solve our doubt.
To show that a given ...
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0answers
328 views
Show that P is a subset of NP
Okay, before I start with the question I would like to point out that I am aware that there are many proofs of this question online. However, I am interested in showing this with the definitions of my ...
2
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1answer
28 views
Analysing the algorithm of a language called CONNECTED in Sipser to show that it belongs to class P
The question and its answer is given in the following picture:
But I do not understand why stage 2 causes at most $n+1$ repetitions, and why stage 3 uses at most $O(n^2)$ steps, and I understand that ...
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2answers
327 views
if traveling salesman problem is decidable in polynomial time, can an actual solution be proposed in polynomial time?
I'm asking because it seems that P problems refer to decision problems rather than actually propose a solution.
8
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0answers
191 views
Are there consequences for P ≠ NP that are unintuitive?
It's often regarded that the most intuitive answer to the question of $P$ vs $NP$ is that $P ≠ NP$. This is often illustrated with some consequences that would follow if $P = NP$ were true. Things ...
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NP-Hard for resolving P=NP [duplicate]
Im studing complexity theory and im reading this question on Quora.
According to what the guy is saying : if we are able to solve a NP-Hard problem in polynomial time we have prooved that P=NP.
But, ...
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1answer
181 views
Could a scientist make money off of the P vs. NP solution?
If someone solved the P vs. NP problem, would they be able to keep it a secret and make money off of it by, say, starting a software or security company? Or would they only be able to publish it for ...
2
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1answer
223 views
Solving diophantine equations — does having a bound on the size of the solution help?
Let's define the following languages over the alphabet $\Sigma=\{0,1\}$:
H10 is the language of all strings that are encoding of diophantine polynomial equation with integer coefficients and $n$ ...
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2answers
1k views
P=NP, isn't it?
Cook and Levin showed in 1971 how deterministically in polynomial time from every non deterministic Turing machine M, that halts in polynomial number of moves/steps, and string w to create the boolean ...
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2answers
321 views
Naive argument that P ≠ NP
Consider the following naïve argument that any algorithm solving SAT must take $\Omega(2^n)$ time in the worst-case scenario.
Let $f(x_1,x_2,\dots,x_n)$ be a Boolean function in conjunctive normal ...
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162 views
Computational Complexity and P vs. NP, A New Insight [closed]
There is a preprint on arXiv that states (in my own words).
If there are three numbers (digits) and task is to add all three numbers. First we well take two number to add, set aside third number. ...
0
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1answer
42 views
Solve Time Complexity problem using Time Hierarchy
I am trying to understand Time Hierarchy. I have an example that is solvable using the rules of Time Hierarchy. I would like an explanation on how to solve so that I may understand better how to use ...
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Consequences from a lower bound of SAT problem
I'm not sure how lower bounds affect the question to the P=NP problem.
I.e. :
Let a SAT instance with a size of n be transformed into an instance of a problem X with a size of n3.
If you find a ...
2
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1answer
138 views
Why doesn't descriptive complexity theory solve P = NP?
According to the Wikipedia page on Descriptive complexity theory:
In the presence of linear order, first-order logic with a least fixed point operator gives P, the problems solvable in ...
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1answer
45 views
Could a modification of Krom's proof system be used to solve 3-SAT in polynomial time?
A literal is a nonzero integer, and we define $\sim x = -x$.
A clause is a nonempty set of literals.
A CNF is a set of clauses.
A K-rule is a pair $(F,C)$ where $F$ is a CNF and $C$ is a clause.
A ...
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1answer
45 views
Given an integer n, print all integers from 1 to 2^n. Why does this not prove that P!=NP? [duplicate]
I only just recently learned about the P=NP problem in introduction to algorithms class, and I'm still trying to wrap my head around it. I thought of this situation while cleaning my room today and ...
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0answers
158 views
If an NP problem is shown to have an exponential lower bound, would that prove that P != NP? [closed]
The Cook-Levin theorem shows that any NP problem is reducible to an NP-complete problem.
Therefore if a polynomial-time algorithm for an NP-complete problem is found, it will mean that all problems ...
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6answers
21k views
If everyone believes P ≠ NP, why is everyone sceptical of proof attempts for P ≠ NP?
Many seem to believe that $P\ne NP$, but many also believe it to be very unlikely that this will ever be proven. Is there not some inconsistency to this? If you hold that such a proof is unlikely, ...
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1answer
92 views
proving that $P\ne NP$ under an assumption
Suppose that $P^{SAT} \not\subseteq coNP$. Prove that $P\ne NP$.
What I did:
Suppose that $P=NP$. Then, $P = coP = NP = coNP$.
We know that $P^P = P$.
Then, by assumption: $P^{NP} = NP = coNP$
...
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1answer
550 views
If P=NP, which two languages are NOT NP-complete?
In my last exam this question got asked and i just cant find a clear answer:
If P=NP, which two languages are NOT NP-complete?
So I assume there are two special languages, but which?
Thanks in ...
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2answers
351 views
Why does this not prove $P\neq NP$?
Fiorini, Massar, Pokutta, Tiwary and De Wolf (Exponential Lower Bounds for Polytopes in Combinatorial
Optimization, Journal of the ACM 62(2):article 17, 2015; PDF, ArXiv) show any linear program that ...
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2answers
611 views
What is the utility of proving P=NP if we can't find an algorithm that can solve any NP problem in polynomial time?
Here we see a very interesting attempt to show that $\mathrm{P} \ne \mathrm{NP}$ by Norbert Blum.
Here we see 116 previous attempts at solving P vs. NP.
Here we see the P vs NP problem defined as:
...
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2answers
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Does this problem offer any insight into $P$ vs $NP$
What is the input of a given hash?
The problem can be verified in polynomial time (using a hash that executed in polynomial time), and I suspect that it may be possible to prove that there is ...
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1answer
265 views
Is the complement of MAX-CLIQUE in NP?
Let $$MAX-CLIQUE = \{\ <G,k>\ |\ G\ is\ an\ undirected\ graph,\ and\ the\ largest\ clique\ of\ G\ has\ k\ vertices\}$$
Does $MAX-CLIQUE\in coNP$? If it does, can you think of a verifier?
...
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1answer
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Could be solved a NP-complete problem in constant time?
Under the assumption that P would be equal to NP, it could exist a NP-complete problem that is solved in constant time?
