How to Play Optimally for Regular Objectives?

We study two-player zero-sum games played on graphs and make contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where the goal of one of the two players is that eventually the sequence of colors along the play belongs to some regular language of finite words. We obtain different characterizations of the chromatic memory requirements for such objectives for both players, from which we derive complexity-theoretic statements: deciding whether there exist small memory structures sufficient to play optimally is NP-complete for both players. Some of our characterization results apply to a more general class of objectives: topologically closed and topologically open sets. These results are based on joint work with Patricia Bouyer, Nathanaël Fijalkow, and Mickael Randour. Contributed talk given by Pierre Vandenhove

Authors

• Pierre Vandenhove

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