The surprizing complexity of generalized reachability games
Résumé
Games on graphs with omega-regular objectives provide a natural model for reactive systems. In this paper, we consider generalized reachability games: given k subsets of vertices, the objective is to reach one vertex of each subset. We show that solving generalized reachability games is PSPACE-complete in general. In the special case where reachability sets are singletons, the problem becomes polynomial. The case where reachability sets have size 2 is still open. We consider one-player restrictions and prove they are NP-complete and polynomial, depending on whether the player tries to ensure or to spoil the generalized reachability objectives. We also investigate memory requirements of both players.
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