Compositional Verification of Timed Statecharts

We propose a compositional proof system for checking real-time properties of a dicrete timed process language TSP with minimal and maximal delays associated to actions. In order to capture the quantitative aspect of time we consider a discrete extension of μ-calculus with freeze quantification over clocks and clock constraints. The language TSP is parametric in the set of basic actions and it is characterized by an operator of process refinement, which permits to suitably model a discrete timed version of statecharts. The proof system is proved to be sound in general and complete for the class of regular finite state processes. It is indeed complete for processes corresponding to statecharts.