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A Kleene-Schützenberger Theorem for Weighted Event-Clock Automata

We present a Kleene-Schützenberger-Theorem for weighted event-clock automata, i.e., we show that the class of recognizable timed series coincides with the class of rational timed series. The result generalizes Kleene’s famous theorem and its extensions to the classes of weighted automata and event-clock automata. For proving the theorem, we use the method of a recent work on the class of weighted timed automata, a proper superclass of weighted event-clock automata, and define a clock semantics which allows for a natural definition of the concatenation operation. We show that for every rational clock series there is a weighted event-clock automaton recognizing the same clock series and vice versa. Finally we obtain a Kleene-Schützenberger-Theorem for the classical semantics by proving that rational (recognizable, respectively) timed series are the projection of rational (recognizable, respectively) clock series.