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:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)