Polylogarithmic independence fools AC0 circuits
M Braverman - Journal of the ACM (JACM), 2008 - dl.acm.org
Journal of the ACM (JACM), 2008•dl.acm.org
We prove that poly-sized AC 0 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.
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.
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.