Fast Asynchronous Systems in Dense Time

A testing scenario in the sense of De Nicola and Hennessy is developed to measure the worst-case eeciency of asynchronous systems using dense time. For all three variants considered, it is shown that one can equivalently use discrete time; in the discrete versions, one variant coincides with an approach based on discrete time in Vog95b], and thus we can clarify the assumptions behind this approach. The resulting testing-preorders are characterized with some kind of refusal traces and shown to satisfy some properties that make them attractive as faster-than relations. The three testing-preorders are incomparable in general, but for some interesting classes of systems implications are shown.