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• W2022983100 abstract "The parallel repetition theorem states that for any Two Prover Game with value at most 1-€ (for € <; 1/2), the value of the game repeated n times in parallel is at most (1 - € <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sup> ) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Ω(n/s)</sup> , where s is the length of the answers of the two provers [24], [17]. For Projection Games, the bound on the value of the game repeated n times in parallel was improved to (1 - € <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> ) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Ω(n)</sup> [23] and this bound was shown to be tight [25]. In this paper we study the case where the underlying distribution, according to which the questions for the two provers are generated, is uniform over the edges of a (bipartite) expander graph. We show that if λ is the (normalized) spectral gap of the underlying graph, the value of the repeated game is at most (1 - € <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> ) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Ω(c(λ)·n/s)</sup> , where c(λ) = poly(λ); and if in addition the game is a projection game, we obtain a bound of (1 - €) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Ω(c(λ)·n)</sup> , where c(λ) = poly(λ), that is, a strong parallel repetition theorem (when λ is constant). This gives a strong parallel repetition theorem for a large class of two prover games." @default.
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• W2022983100 date "2012-06-01" @default.
• W2022983100 modified "2023-09-23" @default.
• W2022983100 title "A Strong Parallel Repetition Theorem for Projection Games on Expanders" @default.
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• W2022983100 doi "https://doi.org/10.1109/ccc.2012.11" @default.
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