Towards proving strong direct product theorems
Computational Complexity
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Strong Parallel Repetition Theorem for Free Projection Games
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Parallel repetition of computationally sound protocols revisited
TCC'07 Proceedings of the 4th conference on Theory of cryptography
A K-provers parallel repetition theorem for a version of no-signaling model
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Distinguishing distributions using Chernoff information
ProvSec'10 Proceedings of the 4th international conference on Provable security
A Counterexample to Strong Parallel Repetition
SIAM Journal on Computing
Parallel Repetition in Projection Games and a Concentration Bound
SIAM Journal on Computing
Derandomized Parallel Repetition Theorems for Free Games
Computational Complexity
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We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz, showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible.