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P (complexity) : ウィキペディア英語版
P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(''n''O(1)), is one of the most fundamental complexity classes. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.
Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable"; in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.
==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 n \in \mathbb, C_n takes ''n'' bits as input and outputs 1 bit
* For all ''x'' in ''L'', C_(x)=1
* For all ''x'' not in ''L'', C_(x)=0
The circuit definition can be weakened to use only a logspace uniform family without changing the complexity class.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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