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NP-complete
(redirected from NP problem)

    Also found in: Wikipedia 0.12 sec.
(complexity)NP-complete - (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.

http://fi-www.arc.nasa.gov/fia/projects/bayes-group/group/NP/.



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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.
The Millennium Problems: The Seven Greatest Unsolved Mathematical ... by Science News
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