2012 IEEE 27th Conference on Computational Complexity (2008)

June 22, 2008 to June 26, 2008

ISSN: 1093-0159

ISBN: 978-0-7695-3169-4

pp: 124-127

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2008.16

ABSTRACT

We prove that the sum of $d$ small-bias generators $L: \F^s \to \F^n$ fools degree-$d$ polynomials in $n$ variables over a prime field $\F$, for any fixed degree $d$ and field $\F$, including $\F = \F_2 =\zo$. Our result improves on both the work by Bogdanov and Viola (FOCS '07) and the beautiful follow-up by Lovett (STOC '08). The first relies on a conjecture that turned out to be true only for some degrees and fields, while the latter considers the sum of $2^d$ small-bias generators (as opposed to $d$ in our result). Our proof builds on and somewhat simplifies the arguments by Bogdanov and Viola (FOCS '07) and by Lovett (STOC '08). Its core is a case analysis based on the \emph{bias} of the polynomial to be fooled.

INDEX TERMS

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CITATION

Emanuele Viola,
"The Sum of d Small-Bias Generators Fools Polynomials of Degree d",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 124-127, 2008, doi:10.1109/CCC.2008.16