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...

• Type: Conference
• Year: 2010
• Where: COCO
• Authors: Ronen Shaltiel
• Keywords: Algorithms, COCO 2010, Free Games, Parallel Repetition, Parallel Repetition Theorem