Strong fairness and ultra metrics

Abstract

We answer an open question of Costa and Hennessy and present a characterization of the infinite fair computations in finite labeled transition systems—without any structure of the states—as cluster points in metric spaces. This technique is applied to reduce the logical complexity of several known fairness concepts from Π 0 3 to Π 0 2 and from Σ 1 1 to Π 0 3, respectively.