E. Asarin, O. Maler, P. Caspi, A Kleene Theorem for Timed
Automata. In this paper we define timed regular
expressions, an extension of regular expressions for
specifying sets of dense-time 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 omega-regular expressions (Buchi's theorem). [Postscript]