On the power of small-depth threshold circuits

Authors:
J. Hastad;M. Goldmann
Affiliations:
R. Inst. of Technol., Stockholm, Sweden;R. Inst. of Technol., Stockholm, Sweden
Venue:
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Year:
1990

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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.