Bounding Average-Energy Games

Patricia Bouyer (1) , Piotr Hofman (2, 1) , Nicolas Markey (3, 1) , Mickael Randour (4) , Martin Zimmermann (5)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
3 SUMO - SUpervision of large MOdular and distributed systems
4 ULB - Département d'Informatique [Bruxelles]
5 Universität des Saarlandes [Saarbrücken]

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound constraint on the energy level (but no upper bound) remained open; in particular, so far there was no known upper bound on the memory that is required for winning strategies. By reducing average-energy games with lower-bounded energy to infinite-state mean-payoff games and analyzing the density of low-energy configurations, we show an almost tight doubly-exponential upper bound on the necessary memory, and that the winner of average-energy games with lower-bounded energy can be determined in doubly-exponential time. We also prove EXPSPACE-hardness of this problem. Finally, we consider multi-dimensional extensions of all types of average-energy games: without bounds, with only a lower bound, and with both a lower and an upper bound on the energy. We show that the fully-bounded version is the only case to remain decidable in multiple dimensions.

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Patricia Bouyer, Piotr Hofman, Nicolas Markey, Mickael Randour, Martin Zimmermann. Bounding Average-Energy Games. FoSSaCS'17, Apr 2017, Uppsala, Sweden. pp.179-195, ⟨10.1007/978-3-662-54458-7_11⟩. ⟨hal-01566431⟩