Circuit lower bounds collapse relativized complexity classes

Abstract

Since the publication of M. Furst et al. (1984) seminal paper connecting AC/sup 0/ with the polynomial hierarchy, it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on Hastad's parity lower bound, we construct an oracle such that P=PH/spl sub//spl oplus/P=EXP.