Abstract
The parallel repetition theorem states that for any two provers one round game with value at most 1 − ε (for ε < 1/2), the value of the game repeated n times in parallel is at most (1 − ε 3)Ω(n/logs) 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 − ε 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 − ε 2)Ω(n/logs) and if in addition the game is a Projection Game we obtain a strong parallel repetition theorem, i.e., a bound of (1 − ε)Ω(n).
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Barak, B., Rao, A., Raz, R., Rosen, R., Shaltiel, R. (2009). Strong Parallel Repetition Theorem for Free Projection Games. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_27
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DOI: https://doi.org/10.1007/978-3-642-03685-9_27
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