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

We prove that the sum of d small-bias generators L : Fs Fn fools degree-d polynomials in n variables over a field F, for any fixed degree d and field F, including F = F2 = {0, 1}. Our result builds on, simplifies, and improves on both the work by Bogdanov and Viola (FOCS '07) and the 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 2d small-bias generators (as opposed to d in our result).

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Emanuele Viola
• Keywords: Algorithms, COCO 2008, Field F, Fs Fn Fools, Small-bias Generators