State explosion is a well-known problem that impedes analysis and testing based on state-space exploration. This problem is particularly serious in real time systems because unbounded time values cause the state space to be infinite even for simple systems. The author presents an algorithm that produces a compact representation of the reachable state space of a real time system. The algorithm yields a small state space, but still retains enough information for analysis. To avoid the state explosion which can be caused by simply adding time values to states, our algorithm uses history equivalence and transition bisimulation to collapse states into equivalent classes. Through history equivalence, states are merged into an equivalence class with the same untimed executions up to the states. Using transition bisimulation, the states that have the same future behaviors are further collapsed. The resultant state space is finite and can be used to analyze real time properties. To show the effectiveness of our algorithm, we have implemented the algorithm and have analyzed several example applications.

The Graphical Communicating Shared Resources, GCSR, is a specification language with a precise, operational semantics for the specification and analysis of real-time systems. GCSR allows a designer to integrate the functional and temporal requirements of a real-time system along with its run-time resource requirements. The integration is orthogonal in the sense that it produces system models that are easy to modify, e.g., to reflect different resource requirements, allocations and scheduling disciplines. In addition, it renders the verification of resource related requirements natural and straightforward. The formal semantics of GCSR allows the simulation of a system model and the thorough verification of system requirements through equivalence checking and state space exploration. This paper reviews GCSR and reports our experience with the production cell case study.