Looking at Mean-Payoff and Total-Payoff through Windows

  • Krishnendu Chatterjee
  • Laurent Doyen
  • Mickael Randour
  • Jean-François Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8172)


We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Laurent Doyen
    • 2
  • Mickael Randour
    • 3
  • Jean-François Raskin
    • 4
  1. 1.IST Austria (Institute of Science and Technology Austria)Austria
  2. 2.LSV - ENS CachanFrance
  3. 3.Computer Science DepartmentUniversité de Mons (UMONS)Belgium
  4. 4.Département d’InformatiqueUniversité Libre de Bruxelles (U.L.B.)Belgium

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