Untimed language preservation in timed systems

Abstract

Timed automata are a model that is extensively used in formal verification of real-time systems. However, their mathematical semantics is an idealization which assumes perfectly precise clocks, but does not correspond to real hardware. In fact, it is known that imprecisions, however small they may be, may yield extra behaviours. Several works concentrated on a relaxation of the semantics of timed automata to model the imprecisions of the clocks. Algorithms were given, first for safety, then for richer linear-time properties, to decide the robustness of timed systems, that is, the existence of a bound on the imprecisions under which the system satisfies a given property. In this work, we study a stronger notion of robustness: we show how to decide whether the untimed language of a timed automaton is preserved under small enough imprecisions, and provide a bound on the imprecision parameter. © 2011 Springer-Verlag GmbH.