Given a two-player one-round game G with value val(G) = (1 - η), how quickly does the value decay under parallel repetition? If G is a projection game, then it is known that we can guarantee val(G⊗n) ≤ (1 - η2)Ω(n), and that this is optimal. An important question is under what conditions can we guarantee that strong parallel repetition holds, i.e. val(G⊗) ≤ (1 - η) Ω(n)? In this work, we show a strong parallel repetition theorem for the case when G's constraint graph has low threshold rank. In particular, for any k ≥ 2, if σk is the k-th largest singular value of G's constraint graph, then we show that val(G ⊗n) ≤(1-√1-σk2/ k·η)Ω(n). This improves and generalizes upon the work of [RR12], who showed a strong parallel repetition theorem for the case when G's constraint graph is an expander. © 2014 Springer-Verlag.
CITATION STYLE
Tulsiani, M., Wright, J., & Zhou, Y. (2014). Optimal strong parallel repetition for projection games on low threshold rank graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8572 LNCS, pp. 1003–1014). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_83
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