Permissive multi-strategies in timed games

This report deals with non-deterministic timed strategies, also called timed multi-strategies, for two-player games played between a controller and the environment on the structure of a timed automaton. The motivation of the concept of multi-strategies in timed systems is to have a certain flexibility of which action to be executed. We introduce a penalty for the controller as a quantitative measure for permissiveness of such strategies. Hereby, the aim is to prevent punctual timed requirements that are not realistic for practical controller-synthesis since realtime systems are subject to perturbation and imprecision of time. We present a game on two slightly different settings with a reachability objective. The aim of the controller is to keep the penalty as low as possible. We propose a fixed point computation for computing the optimal penalty for the controller and show that the most permissive timed multi-strategy for timed automata with one clock is computable in polynomial time. For the general case, we show that the most permissive strategy exists and that memoryless strategies are sufficient. Acknowledgements I would like to express my deepest gratitude to my supervisors Patricia Bouyer-Decitre and Nicolas Markey. They managed to inspire me to the research topic during the class about foundations of real-time systems verification and throughout the internship. I am very thankful for all the fruitful discussions with Patricia and Nicolas. Especially, I want to thank Nicolas for proofreading the report and his generous support throughout the whole internship. Moreover, I am very grateful to have got the opportunity to take part in several scientific meetings and events through the Casting project and LSV. This internship was my greatest research experience so far. Thank you very much Patricia and Nicolas! ∗Ce rapport est rédigé en anglais parce que la connaissance du français de l’auteur n’est pas suffisante.