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

Authors:
Dmitriy Yu. Cherukhin
Affiliations:
Mech. and Math. Faculty, Moscow State University, Moscow, Russia
Venue:
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Year:
2008

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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(n log n) for the size of any circuit computing the cyclic convolution. For depth-2 circuits, a lower bound Ω(n3/2) 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.