Poly-logarithmic Independence Fools AC0 Circuits

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, Baz09], who showed that O(log2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazzi’s theorem.

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Mark Braverman
• Keywords: COCO 2009, Independent Distribution, Poly-size Dnf Formulas, Poly-sized Ac0 Circuits, Theoretical Computer Science