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Summary: Strong Parallel Repetition Theorem for Free
Projection Games
Boaz Barak
Anup Rao
Ran Raz
Ricky Rosen §
Ronen Shaltiel ¶
April 14, 2009
Abstract
The parallel repetition theorem states that for any two provers one round game with value
at most 1 - (for < 1/2), the value of the game repeated n times in parallel is at most
(1- 3
)(n/ log s)
where s is the size of the answers set [Raz98],[Hol07]. For Projection Games the
bound on the value of the game repeated n times in parallel was improved to (1- 2
)(n)
[Rao08]
and was shown to be tight [Raz08]. In this paper we show that if the questions are taken accord-
ing to a product distribution then the value of the repeated game is at most (1 - 2
)(n/ log s)
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