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In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy: PH was first defined by Larry Stockmeyer. It is contained in PPP (the class of problems that are decidable by a polynomial time Turing machine with an access to PP oracle), P PH has a simple logical characterization: it is the set of languages expressible by second-order logic. PH contains almost all well-known complexity classes inside PSPACE; in particular, it contains P, NP, and co-NP. It even contains probabilistic classes such as BPP and RP. P = NP if and only if P = PH. This may simplify a potential proof of P ≠ NP, since it's only necessary to separate P from the more general class PH.
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