Reductions of self-reducible sets to depth-1 weighted threshold circuit classes, and sparse sets

Abstract

Let LT/sub 1/ denote the class of languages accepted by nonuniform families of polynomial size depth-1 circuits with a linear weighted threshold gate at the root. We show that disjunctive self-reducible bd-cylinders that many-one reduce to LT/sub 1/ are in P. It follows that for C/spl isin.