Synthesis of Bounded Integer Parameters for Parametric Timed Reachability Games

We deal with a parametric version of timed game automata (PGA), where clocks can be compared to parameters, and parameter synthesis. As usual, parametrization leads to undecidability of the most interesting problems, such as reachability game. It is not surprising then that the symbolic exploration of the state-space often does not terminate. It is known that the undecidability remains even when severely restricting the form of the parametric constraints. Since in classical timed automata, real-valued clocks are always compared to integers for all practical purposes, we solve undecidability and termination issues by computing parameters as bounded integers. We give a symbolic algorithm that computes the set of winning states for a given PGA and the corresponding set of bounded integer parameter valuations as symbolic constraints between parameters. We argue the relevance of this approach and demonstrate its practical usability with a small case-study.