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In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. [1] Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines.
Checkers if a draw is forced after a polynomial number of non-jump moves [3] Dyson Telescope Game [4] Cross ... Ko-free Go [6] Ladder capturing in Go [7] Gomoku [8 ...
Examples of games that are PSPACE-complete (when generalized so that they can be played on an board) are the games Hex and Reversi. Some other generalized games, such as chess, checkers (draughts), and Go are EXPTIME-complete because a game between two perfect players can be very long, so they are unlikely to be in PSPACE. But they will become ...
It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P = NP: // Algorithm that accepts the NP-complete language SUBSET-SUM. // // this is a polynomial-time algorithm if and only if P = NP. // // "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no".
The class P #P consists of all the problems that can be solved in polynomial time if you have access to instantaneous answers to any counting problem in #P (polynomial time relative to a #P oracle). Thus Toda's theorem implies that for any problem in the polynomial hierarchy there is a deterministic polynomial-time Turing reduction to a ...
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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. [1] It is a special case of hierarchy of bounded alternating Turing machine.
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