Multi-oracle interactive protocols with constant space verifiers

摘要

Multi-oracle interactive protocols are an extension of the Goldwasser-Micali-Rackof model, in which several infinitely powerful provers interact with a single resource-bounded verifier. In this paper we consider the language recognition power of such protocols and prove that a finite state verifier can accept any recursively enumerable set both in the multi-prover submodel of Ben-or, Goldwasser, Kilian, and Wigderson, and in the noisy oracle submodel of Feige, Shamir, and Tennenholtz. Unlike Lipton's single prover construction, our simulation of arbitrary Turing machine computations uses only polynomial overhead and stops with probability 1 (whenever the Turing machine stops). By using the new tehniques, we show that computing the expected payoff of reasonable games of incomplete information is undecidable, thus solving a long-standing open problem posed by Reif.