2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 767-776

W. Maass , Inst. for Inf. Process. Graz, Graz Univ. of Technol., Austria

ABSTRACT

The power of constant depth circuits with sigmoid (i.e., smooth) threshold gates for computing Boolean functions is examined. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size Boolean threshold circuits (i.e., circuits with Boolean threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same Boolean functions as the corresponding circuits with Boolean threshold gates.

INDEX TERMS

polynomially bounded weights, sigmoid threshold gates, smooth threshold gates, depth 2 circuits, computational power, Boolean threshold circuits, constant depth circuits, Boolean functions, constant size circuits, Boolean threshold gates, polynomial size sigmoid threshold circuits

CITATION

W. Maass,
G. Schnitger,
E.D. Sontag,
"On the computational power of sigmoid versus Boolean threshold circuits",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 767-776, 1991, doi:10.1109/SFCS.1991.185447