Time-Progress Evaluation for Dense-Time Automata with Concave Path Conditions

Abstract

The evaluation of successor or predecessor state spaces through time progress is a central component in the model-checking algorithm of dense-time automata. The definition of the time progress operator takes into consideration of the path condition of time progress and usually results in high complexity in the evaluation. Previous algorithms in this aspect usually assume that the original location invariance conditions of an automaton are convex in the dense-time state space. Based on this assumption, efficient algorithms for convex path conditions can be designed for reachability analysis. However, it is not clear whether the path conditions are still convex in the general setting of TCTL model-checking. In this work, we discuss the concept of time-convexity that allows us to relax the restrictions on the application of time-progress evaluation algorithm for convex path conditions. Then we give examples in TCTL model-checking that engenders time-concave path conditions even when the original automaton location invariance conditions are time-convex. Then we present two techniques that allow us to apply the evaluation algorithms for time-convex path conditions to time-concave path conditions. Finally, we report our experiment with the techniques. For some benchmarks, our techniques may enhance the performance of model-checking by an order of magnitude.

The work is partially supported by NSC, Taiwan, ROC under grants NSC 95-2221-E-002-067 and NSC 95-2221-E-002-072.