On the power of small-depth threshold circuits

Abstract

The power of threshold circuits of small depth is investigated. In particular, functions that require exponential-size unweighted threshold circuits of depth 3 when the bottom fan-in is restricted are given. It is proved that there are monotone functions f/sub k/ that can be computed on depth k and linear size AND, OR circuits but require exponential-size to be computed by a depth-(k-1) monotone weighted threshold circuit.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>