Abstract
Higher powers of the Odd Cycle Game has been the focus of recent investigations [3,4]. In [4] it was shown that if we repeat the game d times in parallel, the winning probability is upper bounded by \(1-\Omega({\sqrt{d}\over n\sqrt{\log d}})\), when d ≤ n 2logn. We
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Determine the exact value of the square of the game;
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Show that if Alice and Bob are allowed to communicate a few bits they have a strategy with greatly increased winning probability;
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Develop a new metric conjectured to give the precise value of the game up-to second order precision in 1/n for constant d.
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Show an 1 − Ω(d/nlogn) upper bound for d ≤ nlogn if one player uses a “symmetric” strategy.
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Azimian, K., Szegedy, M. (2008). Parallel Repetition of the Odd Cycle Game. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_58
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DOI: https://doi.org/10.1007/978-3-540-78773-0_58
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