Polylogarithmic independence fools AC0 circuits

Mark Braverman

doi:10.1145/1754399.1754401

Polylogarithmic independence fools AC⁰ circuits

Mark Braverman

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

57 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
Externally published	Yes

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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10.1145/1754399.1754401

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