Circuit Complexity before the Dawn of the New Millennium

. The 1980's saw rapid and exciting development of techniques for proving lower bounds in circuit complexity. This pace has slowed recently, and there has even been work indicating that quite different proof techniques must be employed to advance beyond the current frontier of circuit lower bounds. Although this has engendered pessimism in some quarters, there have in fact been many positive developments in the past few years showing that significant progress is possible on many fronts. This paper is a (necessarily incomplete) survey of the state of circuit complexity as we await the dawn of the new millennium. 1 Superpolynomial Size Lower Bounds Complexity theory long ago achieved its goal of presenting interesting and important computational problems that, although computable, nonetheless require such huge circuits to compute that they are computationally intractable. In fact, in Stockmeyer's thesis, the unusual step was taken of translating an asymptotic result into concrete terms..