Randomness-Efficient Low-Degree Tests and Short PCPs Via Epsilon-Biased Sets

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Randomness-Efficient Low-Degree Tests and Short PCPs Via Epsilon-Biased Sets

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Title: Randomness-Efficient Low-Degree Tests and Short PCPs Via Epsilon-Biased Sets
Author: Vadhan, Salil; Ben-Sasson, Eli; Sudan, Madhu; Wigderson, Avi

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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.
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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.
Published Version: http://dx.doi.org/10.1145/780542.780631
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2961580

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  • FAS Scholarly Articles [7495]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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