Timed Concurrent Game Structures

We propose a new model for timed games, based on concurrent game structures (CGSs). Compared to the classical timed game automata of Asarin et al. [8], our timed CGSs are “more concurrent”, in the sense that they always allow all the agents to act on the system, independently of the delay they want to elapse before their action. Timed CGSs weaken the “element of surprise” of timed game automata reported by de Alfaro et al. [15]. We prove that our model has nice properties, in particular that modelchecking timed CGSs against timed ATL is decidable via region abstraction, and in particular that strategies are “region-stable” if winning objectives are. We also propose a new extension of TATL, containing ATL∗, which we call TALTL. We prove that model-checking this logic remains decidable on timed CGSs. Last, we explain how our algorithms can be adapted in order to rule out Zeno (co-)strategies, based on the ideas of Henzinger et al. [15,21].