Verification of clocked and hybrid systems

This paper presents a new computational model for real-time systems, called the clocked transition system (CTS) model. The c-rs model is a development of our previous timed transition model, where some of the changes are insp ired by the model of timed automata. The new model leads to a simpler style of temporal specification and verification, requiring no extension of the temporal language. We present verification rules for proving safety and liv eness properties of clocked transition systems. All rules are associated wi th verification diagrams. The verification of response properties requires adjustments of the proof rules developed for untimed systems, reflecting th e fact that progress in the real time systems is ensured by the progress of time and not by fairness. The style of the verification rules is very clos e to the verification style of untimed systems which allows the (re)use of verification methods and tools, developed for untimed reactive systems, for proving all interesting properties of real-time systems. We conclude with the presentation of a branching-time based approach for ve rifying that an arbitrary given CTS is non-zeno. Finally, we present an extension of the model and the invariance proof rule for hybrid systems.