Poly-logarithmic Independence Fools AC^0 Circuits

  • Authors:
  • Mark Braverman

  • Affiliations:
  • -

  • Venue:
  • CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
  • Year:
  • 2009

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Abstract

We prove that poly-sized AC^0 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 later given a much simpler proof for Bazzi’s theorem.