In computational 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(x^c) such that A(x,y) = 1}

Algorithm A verifies L in polynomial time.

See also: Complexity classes P and NP and NP-Complete.