License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2010.505
URN: urn:nbn:de:0030-drops-28484
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Chatterjee, Krishnendu ; Doyen, Laurent ; Henzinger, Thomas A. ; Raskin, Jean-Fran├žois

Generalized Mean-payoff and Energy Games

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In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources.

We prove the finite-memory determinacy of generalized energy games and show the inter-reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding
the existence of a winning strategy for the protagonist is NP-complete.

BibTeX - Entry

  author =	{Krishnendu Chatterjee and Laurent Doyen and Thomas A. Henzinger and Jean-Fran{\c{c}}ois Raskin},
  title =	{{Generalized Mean-payoff and Energy Games}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{505--516},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Kamal Lodaya and Meena Mahajan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-28484},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.505},
  annote =	{Keywords: mean-payoff games, energy games, finite memory strategies, determinacy}

Keywords: mean-payoff games, energy games, finite memory strategies, determinacy
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Issue Date: 2010
Date of publication: 13.12.2010

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