NDLI: Parallel repetition: simplifications and the no-signaling case

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Parallel repetition: simplifications and the no-signaling case

Content Provider	ACM Digital Library
Author	Holenstein, Thomas
Abstract	Consider a game where a refereed chooses (x,y) according to a publiclyknown distribution $P_{X}Y,$ 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<1. Raz (SIAM J. Comput. 27, 1998)shows that if the game is repeated n times in parallel, then the probability that Alice and Bob win all games simultaneously is at most $v'^{(n/log(s))},$ 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.
Starting Page	411
Ending Page	419
Page Count	9
File Format	PDF
ISBN	9781595936318
DOI	10.1145/1250790.1250852
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2007-06-11
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Parallel repetition Probabilistically checkable proofs
Content Type	Text
Resource Type	Article

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