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The Sum of d Small-Bias Generators Fools Polynomials of Degree d

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1 Author(s)
Emanuele Viola ; Columbia Univ., New York, NY

We prove that the sum of d small-bias generators L : Fs rarr Fn fools degree-d polynomials in n variables over a prime field F, for any fixed degree d and field F, including F = F2 = {0,1}. 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 of2d 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 bias of the polynomial to befooled.

Published in:

Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on

Date of Conference:

23-26 June 2008