<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)

In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP.Arora and Barak, 2009, pp.

In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e.