Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
W. Maass , Inst. for Inf. Process. Graz, Graz Univ. of Technol., Austria
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.
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
W. Maass, G. Schnitger and E. Sontag, "On the computational power of sigmoid versus Boolean threshold circuits,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 767-776.