Tag: p-vs-np

212 What is the definition of $P$, $NP$, $NP$-complete and $NP$-hard? 2013-02-06T20:38:08.297

89 How not to solve P=NP? 2012-05-17T01:24:29.327

54 What would be the real-world implications of a constructive $P=NP$ proof? 2014-12-29T18:59:34.997

53 If everyone believes P ≠ NP, why is everyone sceptical of proof attempts for P ≠ NP? 2017-10-19T00:17:15.187

27 Are there NP problems, not in P and not NP Complete? 2012-05-12T19:54:22.680

25 Why is Relativization a barrier? 2012-04-14T13:39:56.047

18 Would proving P≠NP be harder than proving P=NP? 2016-01-28T17:09:04.370

15 Does $\mathsf{P} \ne \mathsf{NP}$ imply that $|\mathsf{NP}| > |\mathsf{P}|$? 2012-12-31T17:09:57.310

13 How can P =? NP enhance integer factorization 2012-11-13T19:13:56.870

12 Proving P = NP without mathematical statements / computer program 2013-01-03T10:32:51.870

12 Runtime bounds on algorithms of NP complete problems assuming P≠NP 2014-03-11T20:05:43.997

12 Why do Shaefer's and Mahaney's Theorems not imply P = NP? 2015-06-22T13:06:22.663

11 Why is this argument for $P\neq NP$ wrong? 2015-01-26T18:12:00.907

11 How to prove P$\neq$NP? 2015-12-05T18:50:10.907

10 Proving that if $\mathrm{NTime}(n^{100}) \subseteq \mathrm{DTime}(n^{1000})$ then $\mathrm{P}=\mathrm{NP}$ 2012-11-16T12:57:46.333

10 If one shows that UNIQUE k-SAT is in P, does it imply P=NP? 2014-11-17T14:06:40.830

9 Flaw in my NP = CoNP Proof? 2013-03-12T09:52:11.097

9 P vs NP and the Time Hierarchy 2015-06-23T12:59:47.080

8 Can exactly one of NP and co-NP be equal to P? 2012-06-12T16:45:58.787

8 How to show that the set of machines which accept languages in $\mathrm{NP}\smallsetminus\mathrm P$, is decidable only if $\mathrm P=\mathrm{NP}$? 2012-08-09T11:56:04.413

8 Why does Schaefer's theorem not prove that P=NP? 2015-05-14T10:05:58.173

8 Evolving artificial neural networks for solving NP problems 2015-09-23T13:50:50.170

8 Is detecting easy instances of NP-hard problems easy? 2016-12-16T00:03:53.280

7 How to use an old SAT solver to discover a new one, as is done in The Golden Ticket? 2016-06-01T14:34:40.937

7 Why the need for TSP solvers when there are SAT solvers? 2016-10-03T22:41:15.517

7 What is wrong with this conditional proof of P=NP? 2017-04-08T08:37:02.870

6 Is the open question NP=co-NP the same as P=NP? 2013-02-15T01:38:55.790

6 $1+\epsilon$ approximation for inapproximable problems 2013-03-05T19:27:39.220

6 Does $P \neq NP$ imply $NP \neq PSPACE$? 2015-05-03T21:44:30.680

6 Is there a philosophical counterpart question to P != NP? 2016-07-23T19:35:59.060

6 Why can't we exploite finiteness to prove incompleteness in NP? 2016-09-21T15:11:29.763

6 Polytime algorithm for SUBSET-SUM assuming P=NP 2016-12-18T01:50:18.510

6 What is the utility of proving P=NP if we can't find an algorithm that can solve any NP problem in polynomial time? 2017-08-15T10:26:19.820

5 What would an exponential reduction from an NP-complete problem to P signify? 2012-11-20T15:03:43.400

5 research on OR and AND compression in SAT formulas 2014-05-20T17:47:25.373

5 How is it valid to use oracles in mathematical arguments? 2014-12-09T20:29:51.640

5 Stronger versions of P != NP which better express actual convictions 2016-01-26T10:15:34.740

5 Is anything known about the structure of sets of valuations representable by 3CNF formulas? 2016-01-29T16:00:50.840

5 Why does this not prove $P\neq NP$? 2017-08-18T08:21:58.280

4 Are there are problems in NP that have been shown to be not NP-complete but it is still not known if they are in P or not? 2012-10-17T19:27:32.857

4 Existence of NP problems with complexity intermediate between P and NP-hard 2014-01-06T20:23:25.287

4 Is this language depending on P = NP recursive? 2014-02-25T08:55:19.393

4 Does this mean $P = NP$ 2014-07-08T19:49:22.387

4 What happens to quantum algorithms such as BB84 if P=NP 2014-07-14T14:10:00.903

4 Could an NP-hard problem have a mechanical or physical solution method? 2015-06-07T19:07:54.317

4 Constructing languages in NPI other than through Ladner's Theorem 2015-06-24T16:42:25.697

4 Logarithmic Randomness is Necessary for PCP Theorem 2015-12-10T15:06:41.943

4 Does a polynomial solution for an NP-complete problem that can only be implemented for small N *still* imply P=NP? 2016-06-08T15:43:54.067

4 Why does a reduction from a P-problem to an NP-complete problem not show that P=NP? 2016-11-14T02:12:48.863

4 "P may collapse" vs. Time hierarchy theorem 2016-11-27T11:03:04.053

4 Is there a fundamental reason/limitation, such as $P \not = NP$, that prevents computers from being able to do mathematics (proofs, etc.)? 2017-02-14T11:19:00.007

4 Having problem understanding the formal definition of NP 2017-04-11T10:29:07.157

3 If NP $\neq$ Co-NP then is P $\neq$ NP 2013-01-10T01:36:06.260

3 Is it necessary for NP problems to be decision problems? 2013-02-10T16:30:58.997

3 Reduction from Vertex Cover to an Independent Set problem 2013-05-08T23:39:30.063

3 Provability of NP /= P? 2014-01-30T13:57:04.927

3 What is the implication of the sentence: "if any NP complete problem is p time solvable, then all problems in NP are p time solvable" 2014-12-03T02:29:57.543

3 Is my theorem about $P \neq NP$ correct? 2015-08-24T16:26:54.847

3 co-NP but not NP problems 2017-03-06T07:28:49.483

3 Could a modification of Krom's proof system be used to solve 3-SAT in polynomial time? 2017-11-25T08:00:39.530

2 Implications of polynomial time reductions 2012-12-16T15:28:34.083

2 Proving that if coNP $\neq$ NP then P $\neq$ NP 2013-05-21T09:05:11.783

2 Homomorphism erasing information 2014-09-06T00:31:03.977

2 Subset sum algorithm in O(n³ log n)? 2014-11-25T19:36:31.113

2 Can oracle arguments separate P and NP? 2014-12-05T17:54:15.127

2 If P = NP, why does P = NP = NP-Complete? 2014-12-11T06:12:43.440

2 Could an NP-Hard problem be in P in after a basis transform? 2015-03-15T23:05:29.330

2 $P \neq NP$ and determinism 2015-05-04T14:39:59.307

2 Schaefer's dichotomy theorem and reformulating 3-literal clauses 2015-10-30T16:57:11.730

2 What is the simplest known NP-Complete problem for testing P=NP solutions? 2016-06-10T12:54:39.800

2 Is P = NP when solutions length is polynomially bounded by instance length? 2017-03-18T12:06:43.877

2 Could be solved a NP-complete problem in constant time? 2017-04-16T17:29:29.123

2 proving that $P\ne NP$ under an assumption 2017-09-24T13:23:20.340

2 Why doesn't descriptive complexity theory solve P = NP? 2017-11-30T01:02:37.057

2 Solving diophantine equations -- does having a bound on the size of the solution help? 2018-01-21T16:28:17.197

1 How to prove polynomial time equivalence? 2013-03-22T04:50:15.547

1 Complexity class of Determining Hamiltonian cycle 2013-11-26T04:17:18.607

1 If P != NP, then 3-SAT is not in P 2014-06-10T11:21:38.757

1 A detail on variant of Mahaney's theorem about reductions of sparse languages vs P/NP 2014-07-11T01:28:44.540

1 What are the current known implications of the complexity of Integer Factorization? 2014-07-17T15:42:43.670

1 If P is equal to NP, then what happens to the problems those can be solved in polynomial time? 2015-04-15T19:38:39.587

1 A paper argumenting that P might be equal to NP 2015-04-19T18:06:13.117

1 NP-Hard vs NP-Complete Why NP-complete so important? 2015-06-21T22:16:28.480

1 If an NP-complete problem is shown to have a non-polynomial lower bound, would that prove that P != NP? 2015-08-19T23:26:18.340

1 What is the evidence that P could equal NP? 2015-09-18T10:11:41.870

1 If NP is easy on average then does it mean P=NP? 2016-04-26T09:57:05.027

1 Is valid the notion of infinity for the NP-complete problems? 2017-03-22T19:55:16.897

1 If an NP problem is shown to have an exponential lower bound, would that prove that P != NP? 2017-10-28T19:41:20.117

1 Naive argument that $P \neq NP$ 2018-01-04T16:33:13.380

1 P=NP, isn't it? 2018-01-17T20:25:50.050

0 Recusively Enumerable or Recursive dependent on whether P=NP 2013-01-10T01:41:26.263

0 Why is SAT not in P? 2013-11-07T23:50:44.720

0 What makes it so difficult to prove P =/≠ NP? — The subset sum issue 2014-02-09T23:35:04.740

0 Can P vs NP be independent of accepted axioms? 2014-05-22T19:03:18.710

0 Problem with my proof that NP = coNP? 2014-08-16T17:07:25.497

0 Place 4 notorious problems into 2 diagrams (one assuming P=NP, and the other one assuming P!=NP) 2015-05-31T13:34:59.777

0 Does classification of a problem also require the algorithm used? 2015-11-01T16:13:10.303

0 If EXP = NEXP, can we say anything about P and NP? 2015-12-17T01:36:01.027

0 3SAT with an oracle for expanding the clauses 2015-12-22T10:13:03.020