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In complexity theory, NP ("Non-deterministic Polynomial-time") is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine. Or, equivalently, YES answers are checkable in polynomial time on a deterministic Turing machine given the right information.

A language L belongs to NP if there exists a two input polynomial time algorithm A and a constant c such that

L = {x in {0,1} | ∃ certificate, y with |y| = O(xc) such that A(x,y) = 1}
Algorithm A verifies L in polynomial time.

See Complexity classes P and NP and NP-Complete.

Alternate use: NP is also the ISO country code for Nepal.

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