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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. In this paper, we present 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.
Formal specification, reachability analysis, real-time analysis, state space minimization, timed automata
Date Posted: 17 March 2005
This document has been peer reviewed.