# nondeterministic polynomial time

## nondeterministic polynomial time

(complexity)(NP) A set or property of computational decision problems solvable by a nondeterministic Turing Machine in a
number of steps that is a polynomial function of the size of
the input. The word "nondeterministic" suggests a method of
generating potential solutions using some form of
nondeterminism 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 nondeterministic 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.

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 nondeterministic 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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