Parallel Repetition From Fortification
Name
Moshkovitz_Parallel repetition.pdf
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127.75 KB
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Author(s)
Moshkovitz Aaronson, Dana Hadar
Date Issued
October 2014
Journal
Proceedings of the 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Moshkovitz, Hadar Dana. Parallel Repetition from Fortification. The 55th Annual IEEE Symposium on Foundations of Computer Science, Philadelphia, PA, October 18-21, 2014. pp. 414-423.
Version
Author's final manuscript
Abstract
The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game in terms of the value of the base game and the number of repetitions. In this work we give a simple transformation on games – “fortification” – and show that for fortified games, the value of the repeated game decreases perfectly exponentially with the number of repetitions, up to an arbitrarily small additive error. Our proof is combinatorial and short. As corollaries, we obtain: (1) Starting from a PCP Theorem with soundness error bounded away from 1, we get a PCP with arbitrarily small constant soundness error. In particular, starting with the combinatorial PCP of Dinur, we get a combinatorial PCP with low error. The latter can be used for hardness of approximation as in the work of Hastad. (2) Starting from the work of the author and Raz, we get a projection PCP theorem with the smallest soundness error known today. The theorem yields nearly a quadratic improvement in the size compared to previous work. We then discuss the problem of derandomizing parallel repetition, and the limitations of the fortification idea in this setting. We point out a connection between the problem of derandomizing parallel repetition and the problem of composition. This connection could shed light on the so-called Projection Games Conjecture, which asks for projection PCP with minimal error.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/FOCS.2014.51
