The Free On-line Dictionary of Computing (30 December 2018):

nondeterministic polynomial time
NP 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?  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)