Пятница 8 июля, 18-00, ауд. 106 (совместное заседание с лабораторией им. Чебышева СПбГУ)

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

Докладчик: Mark Braverman (University of Toronto).

Тема: Poly-logarithmic independence fools bounded depth circuits.


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.