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). © 2009 Springer.
CITATION STYLE
Barak, B., Rao, A., Raz, R., Rosen, R., & Shaltiel, R. (2009). Strong parallel repetition theorem for free projection games. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5687 LNCS, pp. 352–365). https://doi.org/10.1007/978-3-642-03685-9_27
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