Complete Problems and Other Properties
Unlike BPP, PP is a syntactic, rather than semantic class. Any polynomial-time probabilistic machine recognizes some language in PP. In contrast, given a description of a polynomial-time probabilistic machine, it is undecidable in general to determine if it recognizes a language in BPP.
PP has natural complete problems, for example, MAJSAT. MAJSAT is a decision problem in which one is given a Boolean formula F. The answer must be YES if more than half of all assignments x1, x2, ..., xn make F true and NO otherwise.
Read more about this topic: PP (complexity)
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