Two-prover one-round proof systems: their power and their problems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Amortized Communication Complexity
SIAM Journal on Computing
Direct product results and the GCD problem, in old and new communication models
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
SIAM Journal on Computing
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Understanding Parallel Repetition Requires Understanding Foams
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
A Counterexample to Strong Parallel Repetition
SIAM Journal on Computing
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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 - Ω(√d/n√log d), when d ≤ n2 log n. We 1. Determine the exact value of the square of the game; 2. Show that if Alice and Bob are allowed to communicate a few bits they have a strategy with greatly increased winning probability; 3. Develop a new metric conjectured to give the precise value of the game up-to second order precision in 1/n for constant d. 4. Show an 1 - Ω(d/n log n) upper bound for d ≤ n log n if one player uses a "symmetric" strategy.