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.

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We consider parametric reachability control problems for real-time systems. We model the plant as an extension of parametric timed automata, i.e., a finite automaton equipped with real-valued clocks constraining its behavior, in which the timing constraints on these clocks can make use of parameters. This extension, which we call parametric game automata (PGA), allows for partitioning the actions in the model between two antagonistic entities: the controller and the environment. The most general problem we study then consists in synthesizing both a controller and values for the parameters such that some control location of the automaton is reachable. It is however well-known that most non-tivial problems on parametric timed automata are undecidable and the classical techniques for the verification (and a fortiori for the control) of timed systems do not terminate in that setting. We therefore provide a subclass of PGA called L/U game automata for which it is decidable. We then consider a backward fixed-point semi-algorithm for solving timed games with reachability objective allowing to compute the most permissive winning strategy. We argue the relevance of this approach and demonstrate its practical usability with a small case-study.

Abstract. Parametric reasoning is particularly relevant for timed models, but very often leads to undecidability of reachability problems. We propose a parametrised version of Interrupt Timed Automata (an expressive model incomparable to Timed Automata), where polynomials of parameters can occur in guards and updates. We prove that different reachability problems, including robust reachability, are decidable for this model, and we give complexity upper bounds for a fixed or variable number of clocks and parameters.