New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
A Parallel Repetition Theorem for Constant-Round Arthur-Merlin Proofs
ACM Transactions on Computation Theory (TOCT)
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We introduce the miss-match form for two-prover one-round proof systems. Any two-prover one-round proof system can be easily modified so as to be in miss-match form. Proof systems in miss-match form have the "projection" property that is important for deriving hardness of approximation results for NP-hard combinatorial optimization problems.Our main result is an upper bound on the number of parallel repetitions that suffice in order to reduce the error of miss-match proof systems from p to $\epsilon$. This upper bound depends only on p and on $\epsilon$ (polynomial in 1/(1-p) and in $1/\epsilon$). Based on previous work, it follows that for any $\epsilon 0,$ NP has two-prover one-round proof systems with logarithmic-sized questions, constant-sized answers, and error at most $\epsilon$.As part of our proof we prove upper bounds on the influence of random variables on multivariate functions, which may be of independent interest.