An Eecient State Space Generation for the Analysis of Real-time Systems

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 innnite over 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 timing information for analysis. To avoid the state explosion which can be caused by simply adding time values to states, our algorithm rst uses history equivalence and transition bisimulation to collapse states into equivalent classes. In this approach, equivalent states have identical observable events although transitions into the states may happen at diierent times. The algorithm then augments the resultant state space with timing relations that describe time distances between transition executions. For example, the relation @(tr 1) + 3 @(tr 2) @(tr 1) + 5 means that transition tr 1 is taken 3 to 5 time units before transition tr 2 is taken. This is used to analyze timing properties such as minimum and maximum time distances between events. To show the eeectiveness of our algorithm, we have implemented the algorithm and have analyzed several example applications.