nondeterministic polynomial time

from The Free On-line Dictionary of Computing (8 July 2008)
nondeterministic polynomial time
NP 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)
    

[email protected]