A Strong Parallel Repetition Theorem for Projection Games on Expanders

The parallel repetition theorem states that for any Two Prover 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/s) , where s is the length of the answers of the two provers [24, 17]. For Projection Games, the bound on the value of the game repeated n times in parallel was improved to (1 - 2 )(n) [23] and this bound was shown to be tight [25]. In this paper we study the case where the underlying distribution, according to which the questions for the two provers are generated, is uniform over the edges of a (bipartite) expander graph. We show that if is the (normalized) spectral gap of the underlying graph, the value of the repeated game is at most (1 - 2 )(c()

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Ran Raz
• Keywords: ECCC 2010, Game, Parallel Repetition, Prover