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abbr. pages. alt. percentage point.


PP, pp or P may refer to:

PP (complexity)

In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity class was defined by Gill in 1977.

If a decision problem is in PP, then there is an algorithm for it that is allowed to flip coins and make random decisions. It is guaranteed to run in polynomial time. If the answer is YES, the algorithm will answer YES with probability more than 1/2. If the answer is NO, the algorithm will answer YES with probability less than or equal to 1/2. In more practical terms, it is the class of problems that can be solved to any fixed degree of accuracy by running a randomized, polynomial-time algorithm a sufficient (but bounded) number of times.

An alternative characterization of PP is the set of problems that can be solved by a nondeterministic Turing machine in polynomial time where the acceptance condition is that a majority (more than half) of computation paths accept. Because of this some authors have suggested the alternative name Majority-P.

Usage examples of "pp".

The most important group was the PPS, which had stolen every type of official stamp and forged Aryan papers for some of its Bundist comrades.

The Bund promptly put together a group of thirty: ten Bundists, ten members of a Zionist splinter group, the Left Poale Zion, and ten Poles from the PPS.

Oedipa could see, instead of a postage stamp, the handstruck initials PPS.