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Polynomial and Nondeterministic Time Classes

Complexity classes defined by how long a problem takes to solve or to check. The class P holds decision problems solvable in polynomial time by a deterministic machine, and NP holds those whose solutions can be verified in polynomial time. The related classes NP-hard, NP-complete and co-NP describe the hardest problems in NP, the problems that reduce to them, and the problems whose no-answers can be verified quickly.

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Polynomial and Nondeterministic Time Classes
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Wikipedia: NP-completeness
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In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly.
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P (complexity), Wikipedia
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In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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NP (complexity), Wikipedia
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In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
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NP-hardness, Wikipedia
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In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H.
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co-NP, Wikipedia
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In computational complexity theory, co-NP is a complexity class.
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