Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Robust locally testable codes and products of codes
Random Structures & Algorithms
Uniform direct product theorems: simplified, optimized, and derandomized
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
The structure of winning strategies in parallel repetition 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
Uniform Direct Product Theorems: Simplified, Optimized, and Derandomized
SIAM Journal on Computing
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The current proof of the probabilistically checkable proofs (PCP) theorem (i.e., ${\cal NP}={\cal PCP}(\log,O(1))$) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra [J. ACM, 45 (1998), pp. 70--122] and Arora et al. [J. ACM, 45 (1998), pp. 501--555].In this paper, we eliminate the need to obtain such strong results on low-degree tests when proving the PCP theorem. Although we do not remove the need for low-degree tests altogether, using our results it is now possible to prove the PCP theorem using a simpler analysis of low-degree tests (which yields weaker bounds). In other words, we replace the strong algebraic analysis of low-degree tests presented by Arora and Safra and Arora et al. by a combinatorial lemma (which does not refer to low-degree tests or polynomials).