Parallel repetition: simplifications and the no-signaling case

  • Authors:
  • Thomas Holenstein

  • Affiliations:
  • Microsoft Research - Silicon Valley Campus, Mountain View, CA

  • Venue:
  • Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
  • Year:
  • 2007

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Abstract

Consider a game where a refereed chooses (x,y) according to a publiclyknown distribution PXY, sends x to Alice, and y to Bob. Withoutcommunicating with each other, Alice responds with a value "a" and Bobresponds with a value "b". Alice and Bob jointly win if a publiclyknown predicate Q(x,y,a,b) holds. Let such a game be given and assume that the maximum probabilitythat Alice and Bob can win is v(n/log(s)), where s is the maximal number of possible responses from Alice and Bob in the initial game, and v' is a constant depending only on v. In this work, we simplify Raz's proof in various ways and thus shorten it significantly. Further we study the case where Alice and Bob are not restricted to local computations and can use any strategy which does not imply communication among them.