ATL with Strategy Contexts and Bounded Memory

Authors:
Thomas Brihaye;Arnaud Costa;François Laroussinie;Nicolas Markey
Affiliations:
Institut de mathématiques, Université de Mons-Hainaut, Belgium;Lab. Spécification & Vééérification, ENS Cachan --- CNRS UMR 8643, France;LIAFA, Univ. Paris 7 --- CNRS UMR 7089, France;Lab. Spécification & Vééérification, ENS Cachan --- CNRS UMR 8643, France
Venue:
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Year:
2009

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Abstract

We extend the alternating-time temporal logics ATL and ATL * with strategy contexts and memory constraints : the first extension makes strategy quantifiers to not "forget" the strategies being executed by the other players. The second extension allows strategy quantifiers to restrict to memoryless or bounded-memory strategies. We first consider expressiveness issues. We show that our logics can express important properties such as equilibria, and we formally compare them with other similar formalisms (ATL , ATL *, Game Logic, Strategy Logic, ...). We then address the problem of model-checking for our logics, especially we provide a PSPACE algorithm for the sublogics involving only memoryless strategies and an EXPSPACE algorithm for the bounded-memory case.