dc.contributor.author | Ben-Sasson, Eli | |
dc.contributor.author | Sudan, Madhu | |
dc.contributor.author | Vadhan, Salil | |
dc.contributor.author | Wigderson, Avi | |
dc.date.accessioned | 2009-05-19T20:32:44Z | |
dc.date.issued | 2003 | |
dc.identifier.citation | Ben-Sasson, Eli, Madhu Sudan, Salil Vadhan, and Avi Wigderson. Randomness-efficient low degree tests and short PCPs via epsilon-biased sets. In Proceedings of the 35th Annual ACM Symposium on the Theory of Computing: San Diego, California, USA, June 9-11, 2003, 612-621. New York, NY: ACM Press. | en |
dc.identifier.issn | 0737-8017 | en |
dc.identifier.uri | http://nrs.harvard.edu/urn-3:HUL.InstRepos:2961580 | |
dc.description.abstract | We present the first explicit construction of Probabilistically Checkable Proofs (PCPs) and Locally TestableCodes (LTCs) of fixed constant query complexity which have almost-linear (=n^{1+o(1)}) size. Such objects were recently shown to exist (nonconstructively) by Goldreich and Sudan [2002]. The key to these constructions is a nearly optimal randomness-efficient version of the low degree test [Rubinfeld & Sudan `96]. In a similar way we give a randomness-efficient version of the BLR linearity test [Blum, Luby, Rubinfeld `93] (which is used, for instance, in locally testing the Hadamard code). The derandomizations are obtained through \eps-biased sets for vector spaces over finite fields. The analysis of the derandomized tests rely on alternative views of \eps-biased sets --- as generating sets of Cayley expander graphs for the low-degree test, and as defining linear error-correcting codes for the linearity test. | en |
dc.description.sponsorship | Engineering and Applied Sciences | en |
dc.language.iso | en_US | en |
dc.publisher | Association for Computing Machinery | en |
dc.relation.isversionof | http://dx.doi.org/10.1145/780542.780631 | en |
dash.license | LAA | |
dc.title | Randomness-Efficient Low-Degree Tests and Short PCPs Via Epsilon-Biased Sets | en |
dc.relation.journal | Proceedings of the Annual ACM Symposium on Theory of Computing | en |
dash.depositing.author | Vadhan, Salil | |
dc.identifier.doi | 10.1145/780542.780631 | * |
dash.contributor.affiliated | Vadhan, Salil | |