• Corpus ID: 14918700

# On Fortification of General Games

@article{Bhangale2015OnFO,
title={On Fortification of General Games},
author={Amey Bhangale and Ramprasad Saptharishi and G. Varma and Rakesh Venkat},
journal={Electron. Colloquium Comput. Complex.},
year={2015},
volume={TR15}
}
• Published 21 April 2015
• Mathematics, Computer Science
• Electron. Colloquium Comput. Complex.
A recent result of Moshkovitz [Mos14] presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in [Mos14] to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel repetition. In this paper, we provide a fix by using a stronger graph that we call fortifiers. Fortifiers are graphs that have both ‘1…

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• Mathematics, Computer Science
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This work gives a simple transformation on games -- "fortification" -- and shows 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.
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Improved bounds for few parallel repetitions of projection games are shown, showing that Raz's counterexample to strong parallel repetition is tight even for a small number of repetitions, and a short proof for the NP-hardness of label cover(1, δ) for all δ > 0, starting from the basic PCP theorem.
• Mathematics, Computer Science
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A parallel repetition theorem for general games with value tending to 0 is proved and the small-value parallel repetition bound obtained is tight.
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A major motivation for the recent interest in the strong parallel repetition problem is that a strong Parallel repetition theorem would have implied that the unique game conjecture is equivalent to the NP hardness of distinguishing between instances of Max-Cut that are at least 1 - isin2 satisfiable from instances that areat most 1 - (2/pi) ldr isin satisfiable.
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We show that a parallel repetition of any two-prover one-round proof system (MIP(2,1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The
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