Abstract

In this paper we define timed regular expressions, an extension of regular expressions for specifying sets of densetime discrete-valued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. The result is extended to !-regular expressions (B uchi's theorem). 1. Introduction Timed automata, i.e. automata equipped with clocks [AD94], have been studied extensively in recent years as they provide a rigorous model for reasoning about the quantitative temporal aspects of systems. Together with realtime logics and process algebras they constitute the underlying theoretical basis for the specification and verification of real-time systems. Kleene's theorem [K56], stating that the regular (or rational) subsets of \Sigma are exactly the recognizable ones (those accepted by finite automata), is one of the cornerstones of automata theory. No such theorem has ...

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