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Lower Bounds for Depth-2 and Depth-3 Boolean Circuits with Arbitrary Gates

  • Dmitriy Yu. Cherukhin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)

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.

Keywords

Boolean function circuit complexity depth lower bound cyclic convolution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dmitriy Yu. Cherukhin
    • 1
  1. 1.Mech. and Math. FacultyMoscow State University, Leninskie GoryMoscowRussia

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