@inproceedings{028df1ef296c4c4e8c28af06188b9349,
title = "A combinatorial consistency lemma with application to proving the PCP theorem",
abstract = "The current proof of the PCP Theorem (i.e., NP=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 and Arora et. al. 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 get rid of 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).",
keywords = "Low-degree tests, NP, Parallelization of probabilistic proof systems, Probabilistically checkable proofs (PCP)",
author = "Oded Goldreich and Shmuel Safra",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1997.; null ; Conference date: 11-07-1997 Through 12-07-1997",
year = "1997",
doi = "10.1007/3-540-63248-4_7",
language = "אנגלית",
isbn = "3540632484",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "67--84",
editor = "Jos{\'e} Rolim",
booktitle = "Randomization and Approximation Techniques in Computer Science - International Workshop, RANDOM 1997, Proceedings",
}