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nexpli
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There are 6 letters in NEXPLI ( E1I1L1N1P3X8 )
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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 * * * * * 2 * * * n * * O * ( * 1 * ) * * * * * * * {\displaystyle 2^{n^{O(1)}}} * . * In terms of NTIME,* * * * * * N * E * X * P * T * I * M * E * * * = * * ⋃ * * k * ∈ * * N * * * * * * N * T * I * M * E * * * ( * * 2 * * * n * * k * * * * * ) * * * {\displaystyle {\mathsf {NEXPTIME}}=\bigcup _{k\in \mathbb {N} }{\mathsf {NTIME}}(2^{n^{k}})} * 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 * * * * * 2 * * p * ( * * | * * x * * | * * ) * * * * * {\displaystyle 2^{p(|x|)}} * on input * * * * ( * x * , * y * ) * * * {\displaystyle (x,y)} * * For all x in L, there exists a string y of length * * * * * 2 * * q * ( * * | * * x * * | * * ) * * * * * {\displaystyle 2^{q(|x|)}} * such that * * * * M * ( * x * , * y * ) * = * 1 * * * {\displaystyle M(x,y)=1} * * For all x not in L and all strings y of length * * * * * 2 * * q * ( * * | * * x * * | * * ) * * * * * {\displaystyle 2^{q(|x|)}} * , * * * * M * ( * x * , * y * ) * = * 0 * * * {\displaystyle M(x,y)=0} * We know * * P ⊆ NP ⊆ EXPTIME ⊆ NEXPTIMEand also, by the time hierarchy theorem, that * * NP ⊊ NEXPTIMEIf 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. |