Fast asynchronous systems in dense time

A testing scenario in the sense of De Nicola and Hennessy is developed to m easure the worst-case efficiency of asynchronous systems using dense time. For all three variants considered, it is shown that one can equivalently us e discrete time; in the discrete versions, one variant coincides with an ap proach based on discrete time in Vogler (CONCUR95, Lecture Notes in Compute r Science, vol. 962, Springer, Berlin, 1995, pp. 299-312), and thus we can clarify the assumptions behind this approach. The resulting testing-preorde rs are characterized with some kind of refusal traces and shown to satisfy some properties that make them attractive as faster-than relations. The thr ee testing preorders are incomparable in general, but for some interesting classes of systems implications are shown. (C) 2001 Elsevier Science B.V. A ll rights reserved.