Timed alternating-time temporal logic

We add freeze quantifiers to the game logic ATL in order to specify real-time objectives for games played on timed structures. We define the semantics of the resulting logic TATL by restricting the players to physically meaningful strategies, which do not prevent time from diverging. We show that TATL can be model checked over timed automaton games. We also specify timed optimization problems for physically meaningful strategies, and we show that for timed automaton games, the optimal answers can be approximated to within any degree of precision.