Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Computational Complexity
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 the odd cycle game
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Graph expansion and the unique games conjecture
Proceedings of the forty-second ACM symposium on Theory of computing
Improved rounding for parallel repeated unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
A Counterexample to Strong Parallel Repetition
SIAM Journal on Computing
Spherical cubes: optimal foams from computational hardness amplification
Communications of the ACM
| Hi-index | 0.02 |
Motivated by the study of Parallel Repetition and also by the Unique Games Conjecture, we investigate the value of the "Odd Cycle Games" under parallel repetition. Using tools from discrete harmonic analysis, we show that after d rounds on the cycle of length m, the value of the game is at most 1 - (1/m) \cdot \Omega(\sqrt d) (for d \leqslant m^2, say). This beats the natural barrier of 1 - \Theta (1/m)^2 \cdot d for Raz-style proofs [31, 21] (see [11]) and also the SDP bound of Feige-Lovasz [14, 17]; however, it just barely fails to have implications for Unique Games. On the other hand, we also show that improving our bound would require proving nontrivial lower bounds on the surface area of high-dimensional foams. Specifically, one would need to answer: What is the least surface area of a cell that tiles \mathbb{R}^d by the lattice \mathbb{Z}^{d}?