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
Read more about this topic: NP (complexity)
Famous quotes containing the words formal and/or definition:
“On every formal visit a child ought to be of the party, by way of provision for discourse.”
—Jane Austen (1775–1817)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)