The compositional specification of timed systems-a tutorial

The analysis of reactive systems requires models representing the system, its interaction with the environment, and taking into account features of the underlying execution structure. It is important that such models are timed if analysis concerns performance, action scheduling or in general, dynamic aspects of the behavior. In practice, timed models of systems are obtained by adding timing constraints to untimed descriptions. For instance, given the functional description of a circuit, the corresponding timed model can be obtained by adding timing constraints about propagation delays of the components; to build a timed model of a real-time software, quantitative timing information concerning execution times of the statements and significant changes of the environment must be added. The construction of timed models of reactive systems raises some important questions concerning their composition and in particular, the way some well-understood constructs for untimed systems can be extended to timed systems. We present an overview of existing executable timed formalisms with a global notion of time, by putting emphasis on problems of compositional description. The results on compositionality have been developed in collaboration with Bornot at Verima