ملخص: 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(log2n)-independent distributions fool poly-size DNF formulas. [Razborov 2008] has later given a much simpler proof for Bazzi’s theorem.

لغة: إنجليزية