Polylogarithmic independence fools AC0 circuits

Mark Braverman

doi:10.1145/1754399.1754401

Polylogarithmic independence fools AC⁰ circuits

Mark Braverman

Computer Science

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

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

Original language	English (US)
Article number	28
Journal	Journal of the ACM
Volume	57
Issue number	5
DOIs	https://doi.org/10.1145/1754399.1754401
State	Published - Jun 2010

All Science Journal Classification (ASJC) codes

Software
Control and Systems Engineering
Information Systems
Hardware and Architecture
Artificial Intelligence

Keywords

Circuit complexity
Lower bounds
Polynomial approximations
Pseudorandomness

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