Zone-based universality analysis for single-clock timed automata

During the last years, timed automata have become a popular model for describing the behaviour of real-time systems. In particular, there has been much research on problems such as language inclusion and universality. It is well-known that the universality problem is undecidable for the class of timed automata with two or more clocks. Recently, it was shown that the problem becomes decidable if the automata are restricted to operate on a single clock variable. However, existing algorithms use a region-based constraint system and suffer from constraint explosion even for small examples. In this paper, we present a zone-based algorithm for solving the universality problem for single-clock timed automata. We apply the theory of better quasi-orderings, a refinement of the theory of well quasi-orderings, to prove termination of the algorithm. We have implemented a prototype based on our method, and checked universality for a number of timed automata. Comparisons with a region-based prototype confirm that zones are a more succinct representation, and hence allow a much more efficient implementation of the universality algorithm. © Springer-Verlag Berlin Heidelberg 2007