Qu'est-ce (qui) est nondeterministic polynomial time - définition

COMPUTATIONAL COMPLEXITY CLASS OF DECISION PROBLEMS SOLVABLE BY A NON-DETERMINISTIC TURING MACHINE IN POLYNOMIAL TIME

NP (complexity class); Nondeterministic polynomial time; NP-problem; NP-Problem; NP class; NP Class; NP-Class; NP-class; Class NP; Complexity class NP; Nondeterministic Polynomial; Nondeterministic polynomial; Np (complexity); NP (class)

nondeterministic polynomial time

<complexity> (NP) A set or property of computational {decision problems} solvable by a nondeterministic Turing Machine in a number of steps that is a polynomial function of the size of the input. The word "nondeterministic" suggests a method of generating potential solutions using some form of nondeterminism or "trial and error". This may take exponential time as long as a potential solution can be verified in polynomial time. NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in {polynomial time}) since a deterministic algorithm can be considered as a degenerate form of nondeterministic algorithm. The question then arises: is NP equal to P? I.e. can every problem in NP actually be solved in polynomial time? Everyone's first guess is "no", but no one has managed to prove this; and some very clever people think the answer is "yes". If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP. See also Co-NP, NP-complete. [Examples?] (1995-04-10)

Polynomial hierarchy

HIERARCHY OF COMPLEXITY CLASSES BETWEEN P AND PSPACE

Polynomial time hierarchy; Polynomial-time hierarchy; NP^NP; Sigma2p

In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP.Arora and Barak, 2009, pp.

https://en.wikipedia.org/wiki/Polynomial_hierarchy

HOMFLY polynomial

TWO-VARIABLE KNOT POLYNOMIAL, GENERALIZING THE JONES AND ALEXANDER POLYNOMIALS

HOMFLY(PT) polynomial; HOMFLY; LYMPHTOFU polynomial; HOMFLYPT polynomial; Homfly polynomial; FLYPMOTH polynomial; HOMFLY invariant

In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e.

https://en.wikipedia.org/wiki/HOMFLY_polynomial

Wikipédia

NP (complexity)

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine.

An equivalent definition of NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine. This definition is the basis for the abbreviation NP; "nondeterministic, polynomial time". These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which consists of a guess about the solution, which is generated in a nondeterministic way, while the second phase consists of a deterministic algorithm that verifies whether the guess is a solution to the problem.

It is easy to see that the complexity class P (all problems solvable, deterministically, in polynomial time) is contained in NP (problems where solutions can be verified in polynomial time), because if a problem is solvable in polynomial time, then a solution is also verifiable in polynomial time by simply solving the problem. But NP contains many more problems, the hardest of which are called NP-complete problems. An algorithm solving such a problem in polynomial time is also able to solve any other NP problem in polynomial time. The most important P versus NP (“P = NP?”) problem, asks whether polynomial-time algorithms exist for solving NP-complete, and by corollary, all NP problems. It is widely believed that this is not the case.

The complexity class NP is related to the complexity class co-NP, for which the answer "no" can be verified in polynomial time. Whether or not NP = co-NP is another outstanding question in complexity theory.

https://en.wikipedia.org/wiki/NP (complexity)