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
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