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(NPC, Nondeterministic Polynomial time complete) A set or property of computational decision problems which is a subset of NP (i.e. can be solved by a nondeterministic Turing Machine in polynomial time), with the additional property that it is also NP-hard. Thus a solution for one NP-complete problem would solve all problems in NP. Many (but not all) naturally arising problems in class NP are in fact NP-complete.

There is always a polynomial-time algorithm for transforming an instance of any NP-complete problem into an instance of any other NP-complete problem. So if you could solve one you could solve any other by transforming it to the solved one.

The first problem ever shown to be NP-complete was the satisfiability problem. Another example is Hamilton's problem.

See also computational complexity, halting problem, Co-NP, NP-hard.

This article is provided by FOLDOC - Free Online Dictionary of Computing (
References in periodicals archive ?
Ritchie asked the faculty to contribute ideas for diagrams, reproducing a currently unsolved mathematical problem in computer science called the 'P versus NP problem.' Ritchie was warned that it is part of the culture at the Cornell campus in Ithaca to scrawl problems on glass walls as though they were whiteboards.
Yet at the present time, if one asks the average mathematician or computer scientist the status of the famous P versus NP problem, he or she will say that it is still open.
This paper will use GA to solve NP problems. A decision problem is called an NP problem if particular examples of it can be solved in polynomial time by a nondeterministic process i.e.
The first, by Martin Davis, professor emeritus at New York University, USA, chronicled the original development of the Davis-Putnam-Loveland-Logemann (DPLL) algorithm and proposed an unorthodox take on the P = NP problem. The second, by Andrei Voronkov, professor at the University of Manchester, UK, addressed new encodings that enable succinct representations of certain combinatorial problems in the Bernays-Schonfinkel fragment of first-order logic.
To represent the book I've decided to discuss the chapter on the one problem an amateur might have a chance of solving: The P vs NP Problem.
These problems require vast amounts of computer time to solve, the amount of time increasing exponentially as the size of the NP problem increases.
(We would not say that an algorithm solves the P = NP problem if it assumes a primitive operation that computes an NP-complete function in polynomial time.)
First, we shall explain the significance of the P versus NP problem and solve it.
Specifically, they are the Riemann hypothesis, which lingers from Hilbert's list, Yang-Mills theory and the mass gap hypothesis, the P Versus NP problem, the Navier-Stokes equations, the Poincaire conjecture, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture.
Most people with these NP problems have impairment that does not appear to affect their daily lives; but standard tests can still detect that impairment.
Number of evolutionary algorithms has been proposed for solving NP problems, e.g.