A Logic for P: Are we Nearly There Yet?

Abstract

Whether or not there is a logic for P is the classic problem of descriptive complexity theory. It has been an open problem for over four decades (since its first formulation by Chandra and Harel [1980]) now and much has been written about it, including surveys and textbook presentations (see, for instance [Ebbinghaus and Flum 1999, Chapter 11]. The problem remains a focus of active research and there have been significant recent developments related to it. These may not be well known outside a specialist group of researchers and one aim of the present article is to bring these to a wider audience. To place the new results in their context, we begin with a wider perspective on the question.