P . Bouyer Updatable Timed Automata , an Algorithmic Approach

The notion of updatable timed automata has been introduced as a natural syntactic extension of classical timed automata. These updatable timed automata allow in particular to represent large classes of real-time systems in a much more concise way. For numerous families of updatable timed automata, the decidability of the emptiness problem has been proved with a suitable extension of Alur and Dill’s region automaton. But this theoretical result does not support a natural implementation, which is not surprising since, even for classical timed automata, the region automaton algorithm is not the algorithm used in tools like UPPAAL or KRONOS. Indeed these tools use instead a so-called zone algorithm and data structures like DBMs. In this paper, we propose a forward analysis algorithm which checks emptiness of decidable updatable timed automata. This algorithm generalizes the zone algorithm for classical timed automata. We also describe a possible implementation using the DBM data structure and we present a complete correctness proof of this algorithm. As a particular case of this result, we obtain a proof of the correctness of the zone algorithm implemented in UPPAAL and KRONOS. Whereas these tools are intensively used, such a proof was, up to our knowledge, still lacking.