Abstract
We provide a subclass of parametric timed automata (PTA) that we can actually and efficiently analyze, and we argue that it retains most of the practical usefulness of PTA for the modeling of real-time systems. The currently most useful known subclass of PTA, L/U automata, has a strong syntactical restriction for practical purposes, and we show that the associated theoretical results are mixed. We therefore advocate for a different restriction scheme: since in classical timed automata, real-valued clocks are always compared to integers for all practical purposes, we also search for parameter values as bounded integers. We show that the problem of the existence of parameter values such that some TCTL property is satisfied is PSPACE-complete. In such a setting, we can of course synthesize all the values of parameters and we give symbolic algorithms, for reachability and unavoidability properties, to do it efficiently, i.e., without an explicit enumeration. This also has the practical advantage of giving the result as symbolic constraints between the parameters. We finally report on a few experimental results to illustrate the practical usefulness of our approach.
Highlights
Real-time systems are ubiquitous, and to ensure their correct design it seems natural to rely on the mathematical framework provided by formal methods
We have presented novel results for the parametric verification of timed systems modeled as parametric timed automata
We have proved that the AF-emptiness problem is undecidable for lower bound/upper bound (L/U)-automata
Summary
Real-time systems are ubiquitous, and to ensure their correct design it seems natural to rely on the mathematical framework provided by formal methods. The model-checking of timed models is becoming ever more efficient. It requires a complete knowledge of the system. If the model of the system is proved wrong or if the environment changes, this complex verification process must be carried out again. It follows that the use of parametric timed models is certainly a very interesting approach for the design of real-time systems. A preliminary version of this work appeared in [20]. It is a challenging issue to define a subclass of parametric timed automata, which retains enough of its expressive power and such that, for both reachability and unavoidability properties, the existence of parameter values is decidable and for which there exist efficient symbolic synthesis algorithms
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