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:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)