Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Small Sample Spaces Cannot Fool Low Degree Polynomials
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Guest Column: correlation bounds for polynomials over {0 1}
ACM SIGACT News
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Random graphs and the parity quantifier
Proceedings of the forty-first annual ACM symposium on Theory of computing
Pseudorandom Bit Generators That Fool Modular Sums
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Small-Bias Spaces for Group Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
On the structure of cubic and quartic polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
Explicit Construction of a Small $\epsilon$-Net for Linear Threshold Functions
SIAM Journal on Computing
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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.