NP (complexity) - Formal Definition

Formal Definition

The complexity class NP can be defined in terms of NTIME as follows:

Alternatively, NP can be defined using deterministic Turing machines as verifiers. A language L is in NP 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 p(|x|) on input (x,y)
  • For all x in L, there exists a string y of length q(|x|) such that M(x,y) = 1
  • For all x not in L and all strings y of length q(|x|), M(x,y) = 0

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