Dynamical Properties of Timed Automata Revisited

We give a generalization of a solution by Puri to the problem of checking emptiness in timed automata with drifting clocks for the case of automata with non-closed guards. We show that non-closed guards pose certain specific problems which cannot be handled by Puri’s algorithm, and propose a new algorithm, based on the idea of “boundary clock regions” of Alur, LaTorre and Pappas. We then give a symbolic algorithm for solving the reachability problem. Our algorithm is based on a symbolic construction of the “neighborhood” of a zone, and on a procedure that, given a set of zones Z, builds the forward propagation of the strongly connected components which can be reached from Z. This improves a symbolic algorithm of Daws and Kordy, due to the ability to handle sets of zones.