Timed Concurrent Game Structures

Abstract

Abstract. 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].

Model-checking for real-time systems

“…This applies for both semantics, with slight differences. It should be noticed that this extends to the explicit-clock version of TCTL, and even to the fragment of explicit-clock TCTL * where formula-clocks are only reset at the level of path quantifiers [66].…”

“…Another approach is to consider TCTL defined with formula clocks as sketched above, and to have it include CTL * . The resulting logic is very expressive while still enjoying a PSPACE model-checking algorithm [66].…”

Natural strategic ability

“…We would also like to look at other natural representations of strategies, including a survey of psychological studies suggesting how people plan and execute their long-term behaviors. Finally, a more complete account of bounded rationality may be obtained by combining bounds on conceptual complexity of strategies (in the spirit of our work here) with their temporal complexity via timing constraints in the vein of [32,14].…”

Timed Temporal Logics

“…This logic then embeds MTL, the extension of LTL with timing constraints, for which model checking is undecidable (see Section 4). An intermediary fragment is defined in [17], with the following syntax:…”

“…Notice that in this fragment, formula clocks may only be reset at the level of state formulas. This allows us to recover decidability of model checking (in exponential space) [17], while being able to express fairness properties.…”