Strong Parallel Repetition Theorem for Free Projection Games

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 )Ω(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 )Ω(n) [Rao08] and was shown to be tight [Raz08]. In this paper we show that if the questions are taken according to a product distribution then the value of the repeated game is at most (1 − 2 )Ω(n/ log s) and if in addition the game is a Projection Game we obtain a strong parallel repetition theorem, i.e., a bound of (1 − )Ω(n) .

• Type: Conference
• Year: 2009
• Where: APPROX
• Authors: Boaz Barak, Anup Rao, Ran Raz, Ricky Rosen, Ronen Shaltiel
• Keywords: Algorithms, APPROX 2009, Game, Parallel Repetition Theorem, Projection Game