Bounds on the Size of Small Depth Circuits for Approximating Majority

In this paper, we show that for every constant 0 < < 1/2 and for every constant d 2, the minimum size of a depth d Boolean circuit that -approximates Majority function on n variables is exp((n1/(2d-2) )). The lower bound for every d 2 and the upper bound for d = 2 have been previously shown by O'Donnell and Wimmer [ICALP'07], and the contribution of this paper is to give a matching upper bound for d 3.

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Kazuyuki Amano
• Keywords: ICALP 2009, Lower Bound, Matching Upper Bound, Theoretical Computer Science