Minimum-Time Reachability in Timed Games

We consider the minimum-time reachability problem in concurrent two-player timed automaton game structures. We show how to compute the minimum time needed by a player to reach a location against all possible choices of the opponent We do not put any syntactic restriction on the game structure, nor do we require any player to guarantee time divergence. We only require players to use physically realizable strategies. The minimal time is computed in part using a fixpoint expression which we show can be used on equivalence classes of a non-trivial extension of the region equivalence relation.