In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time . In terms of NTIME, Alternatively, NEXPTIME can be defined using deterministic Turing machines as verifiers. A language L is in NEXPTIME if and only if there exist polynomials p and q, and a deterministic Turing machine M, such that * For all x and y, the machine M runs in time on input * For all x in L, there exists a string y of length such that * For all x not in L and all strings y of length , We know P ⊆ NP ⊆ EXPTIME ⊆ NEXPTIME and also, by the time hierarchy theorem, that NP ⊊ NEXPTIME If P = NP, then NEXPTIME = EXPTIME (padding argument); more precisely, E ≠ NE if and only if there exist sparse languages in NP that are not in P. (Wikipedia).
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