meaning of polynomial time

1. nondeterministic polynomial time 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? Everyones 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. [Examples?]

Related Words

nondeterministic polynomial time | polynomial-time algorithm |

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