The gap between monotone and non-monotone circuit complexity is exponential

Abstract

A. A. Razborov has shown that there exists a polynomial time computable monotone Boolean function whose monotone circuit complexity is at least nc los n. We observe that this lower bound can be improved to exp(cn1/6-o(1)). The proof is immediate by combining the Alon-Boppana version of another argument of Razborov with results of Grötschel-Lovász-Schrijver on the Lovász - capacity, θ{symbol} of a graph. © 1988 Akadémiai Kiadó.