Exploring Expanders and Derandomization at METRIC 2011 with Mark Braverman

METRIC 2011 Trimester at Institut Henri Poincaré (Paris, France)<br />Workshop on Expanders and derandomization (March 21-25, 2011)<br />Mar 21, 15:00-16:00 - Mark Braverman (U. Toronto)<br />Poly-logarithmic independence fools bounded depth circuits<br />----<br />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.<br /><br />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).<br /><br />The talk will be almost completely self-contained.