On proving lower bounds for circuit size

Abstract

A.A. Razborov's (1989) generalized approximation method, which has the potential of giving tight lower bounds for circuit size, is considered. The method is described in a more intuitive fashion, and its analogy with the ultraproduct construction in model theory is made explicit. The method is extended so that it can be used to lower bound nondeterministic circuit size. Using the proposed framework, a new proof for the exponential monotone size lower bound for the clique function is presented.<>