Probabilistic Robust Timed Games

Solving games played on timed automata is a well-known problem and has led to tools and industrial case studies. In these games, the first player (Controller) chooses delays and actions and the second player (Perturbator) resolves the non-determinism of actions. However, the model of timed automata suffers from mathematical idealizations such as infinite precision of clocks and instantaneous synchronization of actions. To address this issue, we extend the theory of timed games in two directions. First, we study the synthesis of robust strategies for Controller which should be tolerant to adversarially chosen clock imprecisions. Second, we address the case of a stochastic perturbation model where both clock imprecisions and the non-determinism are resolved randomly. These notions of robustness guarantee the implementability of synthesized controllers. We provide characterizations of the resulting games for Büchi conditions, and prove the EXPTIME-completeness of the corresponding decision problems.