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2013-12-16 - Colloque/Présentation - communication orale - Anglais - 44 page(s)

Randour Mickaël , "Looking at Mean-Payoff and Total-Payoff through Windows (invited talk)" in LIAFA verification seminar, Paris, France, 2013

  • Codes CREF : Logique mathématique (DI1170), Théorie des algorithmes (DI1164), Informatique mathématique (DI1160), Informatique générale (DI1162), Théorie de la décision et des jeux (DI1134)
  • Unités de recherche UMONS : Informatique théorique (S829)
  • Instituts UMONS : Institut de Recherche en Technologies de l’Information et Sciences de l’Informatique (InforTech), Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Modélisation mathématique et informatique (CREMMI)
Texte intégral :

Abstract(s) :

(Anglais) 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.