Lower bounds for depth-2 and depth-3 boolean circuits with arbitrary gates

Abstract

We consider depth-2 and 3 circuits over the basis consisting of all Boolean functions. For depth-3 circuits, we prove a lower bound Ω(nlogn) for the size of any circuit computing the cyclic convolution. For depth-2 circuits, a lower bound Ω(n 3/2) for the same function was obtained in our previous paper [10]. Here we present an improved proof of this bound. Both lower bounds are the best known for depth-3 and depth-2 circuits, respectively. © 2008 Springer-Verlag Berlin Heidelberg.