Hybrid models with fairness and distributed clocks

Abstract

Explicit clocks provide a well-known possibility to introduce time into non-real-time theories of reactive systems. This technique is applied here to an approach where distributed systems are modeled with temporal logic of actions as the formal basis, and fairness as the basic force that makes events take place. The focus of the paper is on the formalization and practical proof of hybrid properties of the form “at every moment of time t, Φ(t) holds for X,” where X is a set of objects with distributed clocks, and Φ is a predicate that depends both on the discrete states of x ε X and on time t. The approach is illustrated by a treatment of two well-known examples from the hybrid system literature.