# Action transducers and timed automata

## Abstract

The *timed automaton model* of [13, 12] is a general model for timing-based systems. A notion of *timed action transducer* is here defined as an automata-theoretic way of representing operations on timed automata. It is shown that two timed trace inclusion relations are substitutive with respect to operations that can be described by timed action transducers. Examples are given of operations that can be described in this way, and a preliminary proposal is given for an appropriate language of operators for describing timing-based systems. Finally, justification is given for the definition of implementation based on inclusion of timed trace sets; this is done in terms of a notion of *feasibility* which says that a timed automaton cannot prevent the passage of time.

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