Polylogarithmic independence fools AC0 circuits

Authors:
Mark Braverman
Affiliations:
Microsoft Research New England, Cambridge, Massachusetts, Cambridge, MA
Venue:
Journal of the ACM (JACM)
Year:
2008

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Abstract

We prove that poly-sized AC0 circuits cannot distinguish a polylogarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [1990]. The only prior progress on the problem was by Bazzi [2007], who showed that O(log2 n)-independent distributions fool poly-size DNF formulas. [Razborov 2008] has later given a much simpler proof for Bazzi's theorem.