Mark Braverman

We prove that poly-sized AC0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has ... more >>>

Ravi Boppana, Johan HÃ¥stad, Chin Ho Lee, Emanuele Viola

Let $k=k(n)$ be the largest integer such that there

exists a $k$-wise uniform distribution over $\zo^n$ that

is supported on the set $S_m := \{x \in \zo^n : \sum_i

x_i \equiv 0 \bmod m\}$, where $m$ is any integer. We

show that $\Omega(n/m^2 \log m) \le k \le 2n/m + ...
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Chin Ho Lee, Emanuele Viola

We construct pseudorandom generators with improved seed length for

several classes of tests. First we consider the class of read-once

polynomials over GF(2) in $m$ variables. For error $\e$ we obtain seed

length $\tilde O (\log(m/\e)) \log(1/\e)$, where $\tilde O$ hides lower-order

terms. This is optimal up to the factor ...
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