The Propositional mu-Calculus and Its Use in Model Checking

This paper, and the preceding one, survey two types of formalism which has proved to be particularly successful for eecient automatic verii-cation, or \model checking", of concurrent systems. In the previous paper we considered branching time propositional temporal logics, and now we turn to a more general formalism, the propositional-calculus. The emphasis, as before, is on a broad understanding rather than on technical details. 0 Introduction We saw in the previous paper (Zucker 1992, x2) that many of the temporal operators of CTL turned out to be xed points of certain functionals. In this paper we adopt this approach systematically. We will deene a language L of temporal propositional logic which incorporates least and greatest xed points. Thus, although this paper is self-contained, the previous paper may form a useful introduction to it. We repeat the caveat given in the introduction to the last paper. These two papers are intended mainly as introductions to the eld for non-specialists, and the references should be consulted for further reading. The many worked examples in the following sections may be useful. The present paper should also provide useful background material for the paper (Cleaveland 1992) on the Concurrency Workbench in this volume. This paper has beneeted particularly from Emerson and Lei (1986). 1 Least and greatest xed points We rst give a lightning introduction to the mathematical theory of xed points of functionals.