problem be easy to solve? (more unsolved problems in computer science) The P versus NP problem is a major unsolved problem in theoretical computer science....

as NP, but not necessarily in NP. NP-equivalent Decision problems that are both NP-hard and NP-easy, but not necessarily in NP. NP-intermediate If P and...

Unsolved problem in computer science: P   = ?   N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} (more unsolved problems in computer science)...

be in NP. A problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If some NP-complete...

Look up np in Wiktionary, the free dictionary. NP may refer to: NP (novel), by Japanese author Banana Yoshimoto Nashua-Plainfield Community School District...

Unsolved problem in computer science: ⁠ NP   = ?   co-NP {\displaystyle {\textsf {NP}}\ {\overset {?}{=}}\ {\textsf {co-NP}}} ⁠ (more unsolved problems in computer...

problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems...

co-NP and NP-complete for more details. Fortune showed in 1979 that if any sparse language is co-NP-complete (or even just co-NP-hard), then P = NP, a...

conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the...

states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic...

computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility...

discrete optimization problems are NP-complete, such as the traveling salesman (decision) problem, this is expected unless P=NP. For each combinatorial optimization...

computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational...

cannot be solved by a pseudo-polynomial time algorithm unless P = NP. The strong/weak kinds of NP-hardness are defined analogously. Consider the problem of...

complexity was done by Downey & Fellows (1999). Under the assumption that P ≠ NP, there exist many natural problems that require super-polynomial running...

determine the practical limits on what computers can and cannot do. The P versus NP problem, one of the seven Millennium Prize Problems, is part of the field...

space complexity classes relate to each other in the following way: L⊆NL⊆P⊆NP⊆PSPACE⊆EXPTIME⊆NEXPTIME⊆EXPSPACE (where ⊆ denotes the subset relation). However...

non-deterministic complexity class corresponding to the deterministic class P/poly. NP/poly is defined as the class of problems solvable in polynomial time by...

_{2}&=np(1-p),\\\mu _{3}&=np(1-p)(1-2p),\\\mu _{4}&=np(1-p)(1+(3n-6)p(1-p)),\\\mu _{5}&=np(1-p)(1-2p)(1+(10n-12)p(1-p)),\\\mu _{6}&=np(1-p)(1-30p(1-p...

consistency of P = NP with strong systems). Basically da Costa and Doria define a formal sentence [P = NP]' which is the same as P = NP in the standard...

way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and the space hierarchy theorem, it is known that P ⊊ EXPTIME...

classes NP and co-NP can be defined as N P = ∃ P P {\displaystyle {\mathsf {NP}}=\exists ^{\mathsf {P}}{\mathsf {P}}} , and c o N P = ∀ P P {\displaystyle...

Mahaney that states that if any sparse language is NP-complete, then P = NP. Also, if any sparse language is NP-complete with respect to Turing reductions, then...

solutions, are used. #P-complete problems are at least as hard as NP-complete problems. A polynomial-time algorithm for solving a #P-complete problem, if...

NP-40 (also known as Tergitol-type NP-40 and nonyl phenoxypolyethoxylethanol) is a commercially available detergent with CAS Registry Number 9016-45-9...

always solve an optimization problem to optimality. Unless P = NP, an exact algorithm for an NP-hard optimization problem cannot run in worst-case polynomial...

logic and mathematics? What are the philosophical consequences of the P vs NP problem? What is information? The Church–Turing thesis and its variations...

whether P(x,y) holds given both x and y. This definition does not involve nondeterminism and is analogous to the verifier definition of NP. There is an NP language...

In computational complexity, an NP-complete (or NP-hard) problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose...

{\displaystyle M(x,y)=0} ⁠ We know P ⊆ NP ⊆ EXPTIME ⊆ NEXPTIME and also, by the time hierarchy theorem, that NP ⊊ NEXPTIME If P = NP, then NEXPTIME = EXPTIME (padding...