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Computational Complexity: A Conceptual Perspective
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In two-prover one-round interactive proof systems, nosignaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. The study of multi-prover interactive proof systems with no-signaling provers has been motivated by the study of those with provers sharing quantum states. The relation between them is that no-signaling strategies include all the strategies realizable by provers sharing arbitrary entangled quantum states, and more. It was known that PSPACE ⊆ MIPns(2, 1) ⊆ EXP, where MIPns(2, 1) is the class of languages having a two-prover one-round interactive proof system with no-signaling provers. This paper shows MIPns(2, 1) = PSPACE. This is proved by constructing a fast parallel algorithm which approximates within an additive error the maximum winning probability of no-signaling players in a given cooperative two-player one-round game. The algorithm uses the fast parallel algorithm for the mixed packing and covering problem by Young (FOCS 2001).