A Non-standard Approach to Operational Semantics for Timed Systems

Abstract

Operational semantics for linearly and quantitatively timed systems depend crucially on the model of time chosen. Two approaches are common: (a) Discrete models of time isomorphic to the natural numbers. Well established discrete formalisms can be used to describe the dynamical behavior of the system and time is uniform, but sequential refinement and composition of systems designed for different time scales are dificult, and continuous changes can not be well represented. (b) Hybrid models as sequences of intervals of the real numbers. Discrete events happen where such an interval ends (and, typically, the next one starts) and are assumed to take no time. Continuous changes take place during intervals. Point intervals are used to model consecutive discrete steps without an interveningcon tinuous phase. Hybrid models can express the combination of continuous and discrete changes and allow sequential refinement of discrete steps. There are no problems for composition of systems because of differing bases of time. But this model of time is dense and non-uniform, and this makes reasoningm ore dificult.