Probabilistic Timed Simulation Verification and Its Application to Stepwise Refinement of Real-Time Systems

Today, timed automaton is the standard tool for specifying and verifying real-time systems. On the other hand, recently, probabilistic timed automata have been developed in order to express the relative likelihood of the system exhibiting certain behavior. In this paper, we develop the verification method of timed simulation relation of probabilistic timed automata, and apply this method to stepwise refinement developments of real-time systems. This kind of simularity is a valuable theoretical tool to prove soundness of refinements.