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2010
Springer

Derandomized Parallel Repetition Theorems for Free Games

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Derandomized Parallel Repetition Theorems for Free Games
—Raz’s parallel repetition theorem [21] together with improvements of Holenstein [12] shows that for any two-prover one-round game with value at most 1 − (for ≤ 1/2), the value of the game repeated n times in parallel on independent inputs is at most (1− )Ω( 2n ) where is the answer length of the game. For free games (which are games in which the inputs to the two players are uniform and independent) the constant 2 can be replaced with 1 by a result of Barak, Rao, Raz, Rosen and Shaltiel [1]. Consequently, n = O(t ) repetitions suffice to reduce the value of a free game from 1 − to (1 − )t , and denoting the input length of the game by m, if follows that nm = O(t m ) random bits can be used to prepare n independent inputs for the parallel repetition game. In this paper we prove a derandomized version of the parallel repetition theorem for free games and show that O(t(m+ )) random bits can be used to generate correlated inputs such that the value of the parallel repetiti...
Ronen Shaltiel
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where COCO
Authors Ronen Shaltiel
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