Temporal Logic for Stabilizing Systems

Abstract

. This paper links two formerly disjoint research areas: temporal logic and stabilization. Temporal logic is a widely acknowledged language for the specification and verification of concurrent systems. Stabilization is a vitally emerging paradigm in fault tolerant distributed computing. In this paper we give a brief introduction to stabilizing systems and present fair transition systems for their formal description. Then we give a formal definition of stabilization in linear temporal logic and provide a set of temporal proof rules specifically tailored towards the verification of stabilizing systems. By exploiting the semantical characteristics of stabilizing systems the presented proof rules are considerably simpler than the general temporal logic proof rules for program validity, yet we prove their completeness for the class of stabilizing systems. These proof rules replace the hitherto informal reasoning in the field of stabilization and constitute the basis for machine-supported ve..