Definition
A language L is in P if and only if there exists a deterministic Turing machine M, such that
- M runs for polynomial time on all inputs
- For all x in L, M outputs 1
- For all x not in L, M outputs 0
P can also be viewed as a uniform family of boolean circuits. A language L is in P if and only if there exists a polynomial-time uniform family of boolean circuits, such that
- For all, takes n bits as input and outputs 1 bit
- For all x in L,
- For all x not in L,
The circuit definition can be weakened to use only a logspace uniform family without changing the complexity class.
Read more about this topic: P (complexity)
Famous quotes containing the word definition:
“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)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)