Questions tagged [p-vs-np]

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Is P=NP either false or independent of ZFC axioms of mathematics?

A discussion is given on the home page of professor S Gill Williamson UCSD CSE but not resolved there: search for "s gill williamson" seventh topic down.
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0 answers
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Proof Closer String/Consensus String/Center String is NP-hard

Given are n gene sequences (words over the alphabet {A, T, C, G}), each of length m. Find a gene sequence (of length m) that minimizes the maximum distance to all given gene sequences. Here, distance ...
3 votes
1 answer
855 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-...
2 votes
0 answers
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How can the approximation algorithm of one NP-complete problem be used to prove "the class P would be the same as the class NP"?

Recently, when I self-learnt Discrete Mathematics and Its Applications 8th by Kenneth Rosen, I had some questions about some statements in it. Fur- thermore, if a polynomial worst-case time ...
0 votes
2 answers
75 views

Is there a challenge with which one could reasonably show to have found a feasible polynomial algorithm for an NP problem?

Say there is someone claiming to have solved P vs NP, by finding a (computationally feasible, i.e. no huge constants) polynomial solution to a problem in NP: Apart from a formal proof, is there any ...
-1 votes
1 answer
35 views

Natural combinatorial property in Natural Proofs

From Natual Proofs Specifically, natural proofs prove lower bounds on the circuit complexity of boolean functions. A natural proof shows, either directly or indirectly, that a boolean function has a ...
1 vote
1 answer
67 views

Does $\mathsf{P} = \mathsf{NP}$ imply $\mathsf{PO} = \mathsf{NPO}$?

The class $\mathsf{NPO}$ is defined as optimization problems such that the corresponding decision problems defined with a threshold are in $\mathsf{NP}$. Let $A$ be an optimization problem and $B$ a ...
0 votes
1 answer
49 views

3 Processor Scheduling

A set of n independent tasks, each having integer execution times, are to be executed using three identical processors. A task can be executed in any of the three processors. Develop a sequential ...
0 votes
2 answers
137 views

( Soft question ) P vs NP - is such a situation possible?

Currently P vs NP is the holy grail of theoretical computer science. And the nature of the problem is as such that if actually P = NP is proved then most of the proofs for mathematical statements ...
-1 votes
2 answers
343 views

What are the practical examples of Semidecidable problems? Is NP problem a semidecidable problem?

I am going through a Turing machine topic. I know about decidable, semi decidable, and decidable problems. But honestly speaking, I did not get any practical examples of Semidecidable problems. Can ...
0 votes
1 answer
30 views

Is « Does exist at least one function $u$ such that $f(u(0)) \ne g(u(0))$? » an NP problem? or a P problem?

$f$ and $g$ being known functions. We suppose that the problem is solvable. To me, for the moment, this question, if a decision problem it is or can be, is more an NP rather than a P problem, because ...
1 vote
1 answer
54 views

If the Navier-Stokes equations problem is a computable problem, for example a set/language called "L", what are the elements of L?

First, can the Navier-Stokes problem be a formal computable one? like a P problem? Then, how to define the corresponding language? Would it only be the set of equations, or something else? Then, could ...
0 votes
3 answers
104 views

If X is poly-time reducible to Y and X is in P, then Y is in P

The answer I found on the Internet is false. But my argument is that if I know that X is poly-time reducible to Y, which means I can use Y as a sub-routine to solve X, i.e., if I have a blackbox of Y ...
1 vote
2 answers
77 views

Are there problems in NP that would solve P vs NP, but are not NP complete

NP-complete problems are the "hardest problems" in NP. This means that all other problems in NP reduce (in polytime) to these problems. A consequence of this is if we were to find some ...
0 votes
1 answer
74 views

3sat to clique reduction program

I am searching for a program to convert 3sat to clique problem. I tried following links https://www.geeksforgeeks.org/maximal-clique-problem-recursive-solution/ https://www.geeksforgeeks.org/find-all-...
0 votes
0 answers
31 views

Does the following down-voted answer not answer the question "Why does Schaefer's theorem not prove that P=NP?"?

Does the following highly down-voted answer not answer the question "Why does Schaefer's theorem not prove that P=NP?"? If not, why not? Marek, V. Wiktor. Introduction to Mathematics of ...
1 vote
0 answers
63 views

Is NP a subring of the 2-adic integers?

Let me take the set $A = \{1, 2\}$ as the alphabet. By the bijective binary numeral system, $A^*$ has one-to-one correspondence to the set of nonnegative integers $\mathbb{N}$. As such, each language $...
12 votes
3 answers
2k views

Why does Schaefer's theorem not prove that P=NP?

This is probably a stupid question, but I just don't understand. In another question they came up with Schaefer's dichotomy theorem. To me it looks like it proves that every CSP problem is either in P ...
0 votes
1 answer
37 views

Is there an oracle $A$ with $P^A = NP^A$, but $EXP^A \not= NEXP^A$?

Is there an oracle $A$ with $P^A = NP^A$, but $EXP^A \not= NEXP^A$ ? I found a proof with padding arguments (wikipedia), that $$ P = NP \Rightarrow EXP = NEXP $$ If an oracle $A$ exists with $P=NP$ ...
1 vote
1 answer
165 views

What could $P = NP$ imply about arbitrary Turing machines?

My question: What $P \not= NP$ or $P = NP$ could imply about arbitrary Turing machines and arbitrary computations? I assume that a partial and incomplete, but objective answer to this question exists ...
-4 votes
2 answers
273 views

Review my proof that Co-NP != P

The idea is to pick a problem category in Co-NP, where the correct answer is hard to verify because of circuit complexity, express it as 1-in-k SAT formula, and show there also exists a short ...
0 votes
1 answer
41 views

Could there theoretically exist a problem $A$ which is in $co$-$NP$, but its complement $A^{C}$ is $EXPTIME$-complete?

I was reading a bit about $NP$-problems and how it is widely assumed that $NP\neq co$-$NP$. This also implies that the complement of $NP$-complete problems are not in $NP$. What is known is that the ...
1 vote
0 answers
160 views

if L is in NP-Complete and its complement is also in NP does that mean L is in P? (meaning that P=NP)

$L^\complement$ = the complement of L is it true that if $L\in NPComplete $ and $L\leq_p L^\complement \rightarrow P=NP$ basically asking if the following statements are correct $if (L\in NPComplete ) ...
2 votes
1 answer
318 views

if P = NP, does it mean that P = NP = NP-complete?

Lets assume P = NP, so all problems in NP are decidable in polynomial time, Therefore I can solve all problems in NP in polynomial claiming P = NP = NPC. But then, how come Σ* belongs to P = NPC ...
0 votes
0 answers
20 views

reduction from partition to N3DM or balanced 3 partition problem

I want to know how can I reduce Subset Sum or Partition problem to N3DM problem in which each set has exactly 3 elements and same sum. N3DM Problem: https://en.wikipedia.org/wiki/Numerical_3-...
3 votes
3 answers
226 views

Question about the Relativization barrier

Baker, Gill, and Solovay has shown in their famous paper, that there are oracles $A$ and $B$ with $P^A = NP^A$ and $P^B \not= NP^B$. So, one can't solve the $P$ vs. $NP$ Problem with methods like ...
1 vote
1 answer
50 views

Does $\texttt{Oracle-SAT} \leq_T^P \texttt{SAT} \iff \texttt{P} \neq \texttt{NP}$, and is this possible?

The problem of Oracle-SAT is given below: Given oracle query access to some machine, $U$ that has $2^N$ inputs, determine if there is an input such that the machine accepts. This is very similar to ...
0 votes
0 answers
35 views

Is Quantum Search (SAT with only oracle access) NP-hard (and not NP-complete)?

Quantum search differs from the standard boolean SAT as it is restricted to only oracle calls to a circuit (or CNF formula). Where SAT gives us the structure of a formula (however loosely defined that ...
0 votes
2 answers
42 views

Are there any other language classes of time complexity between the P language class and the NP language class?

$P$ is the language class that is decidable in polynomial time by a deterministic Turing machine. $NP$ is a language class that is decidable in polynomial time by non-deterministic Turing machines and ...
-1 votes
2 answers
60 views

Is One Way TSP NP-Complete?

I know that finding the optimal solution to One Way TSP (TSP but the salesman does not have to return to his original city) is NP-Hard, but is it NP-Complete? I ask this because I recently found a ...
0 votes
1 answer
178 views

If P=NP then all languages in P are NP-complete?

I know that if $P=NP$ then all of the languages in $NP$ are $NP-Complete$, but what about those in $P$? I assume yes, because $P \subseteq NP$, but I just want to check. Thanks!
0 votes
4 answers
220 views

Why do some "common sense" $P \ne NP$ arguments seem to disregard high-degree polynomials?

I've seen arguments for $P \ne NP$ that rely on certain intuitions about how the real world actually is, generally making the point that it "makes sense" that there exist problems which have ...
0 votes
1 answer
75 views

Using undecidability to prove P != NP

Given the challenge of proving algorithmic bounds on the likes of 3-SAT to resolve P versus NP, I wondered whether it might be possible to use undecidability within an NP problem to ensure that we can ...
0 votes
1 answer
88 views

Understanding P, NP with an example decision problem

I was reading the definitions of p vs np in [this post] (What is the definition of P, NP, NP-complete and NP-hard?) and I was wondering about how to classify the example decision problem where you ...
-1 votes
2 answers
60 views

Does superpolynomial lower bounds of a problem in $NP$ mean that $P \neq NP$?

If one proves that the lower bounds of an $NP$ problem, are not bounded by any polynomial, is this enough to prove that $P$ does not equal $NP$?
3 votes
1 answer
117 views

Why is this a flawed counterexample to P=NP?

I apologize in advance for asking this, since I'm sure this site is flooded by amateurs like me asking about P and NP. If there's a better platform to ask this on, please let me know, but this ...
1 vote
3 answers
116 views

Problems Solvable in Poly time but not verifiable in Poly time

I was just wondering if there exists problems that are solvable in polynomial time (a correct solution can be found in polynomial time) but not verifiable in polynomial time. My professor says no, but ...
2 votes
2 answers
200 views

Why does showing that a NP problem is not NP-complete implies P$\neq$NP?

I found in this answer that if a problem is shown to be NP but not NP-complete then P$\neq$NP. What is the argument to prove this statement?
1 vote
1 answer
30 views

In NP-hardness, can any category reduce to itself? How can you intuitively explain which categories reduce to the others?

I'm trying to understand how problems in NP-hardness reduce to one another. As I understand it now, if X reduces to Y, Y is at least as hard as X. What I think that means, and would like confirmed or ...
0 votes
1 answer
47 views

P = NP: Doesn't a search generate more information than a check?

I feel like I am understanding P ≠ NP fairly well, but there is one issue I feel like I am missing. It seems like a search for an answer generates information that a check does not. Is this a correct ...
0 votes
1 answer
156 views

Why solving #2SAT in polynomial time implies P = NP?

The wikipedia article for #P states that if we have a polynomial-time algorithm for a #P-complete problem, P = NP is true. As #2SAT is #P-complete, this would mean that providing a polynomial-time ...
-2 votes
2 answers
389 views

Prove or Disprove, 3SAT ≤p 2SAT, then P = NP

I know that 3SAT is in NP and 2SAT is in P. And 2SAT can reduce to 3SAT just says 3SAT is strictly harder than 2SAT, so I don't think this proves P = NP, but it doesn't seem to disprove it either.
0 votes
1 answer
64 views

Set of Turing machines that accepts at least one input in bounded time

What is known about the languages: $$S_f = \{ [M] \ | \ \exists{x} \ \text{s.t.} \\ M \ \text{accepts} \ x \ \text{in} \ f(|[M]|) \ \text{steps}, \\ \ |x| \leq f(|[M]|) \}$$ I used to think that in ...
1 vote
1 answer
59 views

Is ANF-SAT P or NP?

Given a finite set of equations in ANF, for example: $$ \begin{cases} (x_1 \land x_2) \oplus (x_1 \land x_3 \land x_4) \oplus 1 = 0 \\ x_3 \oplus (x_2 \land x_3 \land x_4) = 0 \\ (x_1 \land x_4) \...
4 votes
1 answer
65 views

Are there problems in $P$, long suspected to be $NPC$ (or $NPI$)?

One of the most compelling arguments people cite for believing $P \ne NP$ is that there are many problems of both theoretical and practical significance for which an efficient solution has eluded many ...
0 votes
1 answer
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P vs. NP problem and understanding "worst case complexity"

Suppose that $P \not= NP$. Then my understanding is not all instances of NP-complete problems can be solved in polynomial time. That is for every NP-complete problem, there are a colleciton of ...
0 votes
1 answer
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Unpacking the notion of "hardest instances" for NP-complete problems

Suppose, for the sake of argument, that it was proved that $P \not= NP$. Then, this would imply that for every $NP$-complete problem, there is a "hardest instance" of the problem that ...
0 votes
0 answers
52 views

Could we know what's the total number of unsatisfiable 3SAT formulas for a given n variables?

given some $n$ variables I would be interested to know what is the count of all 3SAT formulas under $n$ that are unsatisfiable. An example of all 3SAT forumlas under $n=3$ is the following: $$ ( x \...
10 votes
6 answers
6k views

Evolving artificial neural networks for solving NP problems

I've recently read a really interesting blog entry from Google Research Blog talking about neural network. Basically they use this neural networks for solving various problems like image recognition. ...
0 votes
2 answers
63 views

How could NP-complete problems be in P?

I've learned some basics about P and NP. Please excuse if the following is not very precise. I've read that NP-complete problems are the hardest problems in NP. (Is that correct?) But now I'm ...

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