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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.
[Examples?]
(1995-04-10)
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Nearby terms:
nondeterminism « nondeterministic « nondeterministic automaton « nondeterministic polynomial time » Nondeterministic Turing Machine » non-impact printer » non-interlaced
This article was derived from the Free Online Dictionary of Computers and is available under ther terms of the GNU Free Documentation License.
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