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Computing (FOLDOC) dictionary
nondeterministic polynomial time
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complexity (NP) A set or property of computational decisionproblems 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 polynomialtime) 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".