The complexity class NP can be defined in terms of NTIME as follows:
where is the set of decision problems that … See more

Many computer science problems are contained in NP, like decision versions of many search and optimization problems.
In order to explain the verifier-based definition of NP, consider the subset sum problem: … See more

NP is closed under union, intersection, concatenation, Kleene star and reversal. It is not known whether NP is closed under complement (this question is the so-called "NP versus co-NP" question). See more

Because of the many important problems in this class, there have been extensive efforts to find polynomial-time algorithms for problems in NP. However, there remain a large number of problems in NP that defy such attem… See more

The two definitions of NP as the class of problems solvable by a nondeterministic Turing machine (TM) in polynomial time and the class of problems verifiable by a deterministic Turing machine in polynomial time are eq… See more

NP contains all problems in P, since one can verify any instance of the problem by simply ignoring the proof and solving it. NP is contained in PSPACE—to show this, it suffices to construct a PSPACE machine that loops o… See more