Laboratory of Mathematical Logic at PDMI

Пятница, 8 июля, ауд. 106. Начало в 18:00.

Докладчик: Mark Braverman (University of Toronto).

Тема: Poly-logarithmic independence fools bounded depth circuits.

Abstract

A Boolean circuit of depth $d$ is a circuit comprised of AND, OR and NOT gates arranged in at most $d$ layers. This class of circuits is one of the few complexity classes where unconditional lower bounds, i.e. computational impossibility results exist. Many of the bounds follow from a deep connection between bounded-depth circuits and low-degree multivariate polynomials.

In this talk we will discuss some of these connections. We will then present a proof of the 1990 Linial-Nisan conjecture on the computational power of bounded-depth circuits. The conjecture stated that bounded-depth Boolean circuits of size $poly(n)$ cannot distinguish inputs drawn from a $k$-wise independent distributions from uniform inputs, where $k=poly(\log n)$. The talk will be almost completely self-contained.