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)
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—William James (1842–1910)
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