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:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“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)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)