Parameterized parallel computing and first-order logic

Abstract

The relationship between the complexity class AC0 and first-order logic transfers to the parameterized class AC0, the parameterized analogue of AC0. In the last years this relationship has turned out to be very fruitful. In this paper we survey some of the results obtained, mainly applications of logic to complexity theory. However the last section presents a strict hierarchy theorem for first-order logic obtained by a result of complexity theory.