Bounding Average-Energy Games

  • Patricia Bouyer
  • Piotr Hofman
  • Nicolas Markey
  • Mickael Randour
  • Martin Zimmermann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)

Abstract

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 prove that the winner of average-energy games with lower-bounded energy can be determined in doubly-exponential time. We also prove Open image in new window -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.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Piotr Hofman
    • 1
    • 2
  • Nicolas Markey
    • 1
    • 3
  • Mickael Randour
    • 4
  • Martin Zimmermann
    • 5
  1. 1.LSV, CNRS & ENS CachanUniversité Paris SaclayCachanFrance
  2. 2.University of WarsawWarszawaPoland
  3. 3.IRISA, CNRS & INRIA & U. Rennes 1RennesFrance
  4. 4.Computer Science DepartmentULB - Université Libre de BruxellesBrusselsBelgium
  5. 5.Reactive Systems GroupSaarland UniversitySaarbrückenGermany

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