<complexity> (NP) A set or property of computational decision problems solvable by a non-deterministic Turing Machine in a number of steps that is a polynomial function of the size of the input. The word "non-deterministic" suggests a method of generating potential solutions using some form of non-determinism or "trial and error". This may take exponential time as long as a potential solution can be verified in polynomial time.
NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in polynomial time) since a deterministic algorithm can be considered as a degenerate form of non-deterministic algorithm. The question then arises: is NP equal to P? I.e. can every problem in NP actually be solved in polynomial time? Everyone's first guess is "no", but no one has managed to prove this; and some very clever people think the answer is "yes".
If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP.
See also Co-NP, NP-complete.
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