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Concurrent Parameterized Games

Authors Nathalie Bertrand , Patricia Bouyer , Anirban Majumdar



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Author Details

Nathalie Bertrand
  • Univ. Rennes, Inria, CNRS, IRISA, Rennes, France
Patricia Bouyer
  • LSV, CNRS & ENS Paris-Saclay, Univ. Paris-Saclay, Cachan, France
Anirban Majumdar
  • Univ. Rennes, Inria, CNRS, IRISA, Rennes, France
  • LSV, CNRS & ENS Paris-Saclay, Univ. Paris-Saclay, Cachan, France

Acknowledgements

We thank Christoph Haase for insightful discussions on semilinear sets.

Cite AsGet BibTex

Nathalie Bertrand, Patricia Bouyer, and Anirban Majumdar. Concurrent Parameterized Games. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 31:1-31:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSTTCS.2019.31

Abstract

Traditional concurrent games on graphs involve a fixed number of players, who take decisions simultaneously, determining the next state of the game. In this paper, we introduce a parameterized variant of concurrent games on graphs, where the parameter is precisely the number of players. Parameterized concurrent games are described by finite graphs, in which the transitions bear regular languages to describe the possible move combinations that lead from one vertex to another. We consider the problem of determining whether the first player, say Eve, has a strategy to ensure a reachability objective against any strategy profile of her opponents as a coalition. In particular Eve’s strategy should be independent of the number of opponents she actually has. Technically, this paper focuses on an a priori simpler setting where the languages labeling transitions only constrain the number of opponents (but not their precise action choices). These constraints are described as semilinear sets, finite unions of intervals, or intervals. We establish the precise complexities of the parameterized reachability game problem, ranging from PTIME-complete to PSPACE-complete, in a variety of situations depending on the contraints (semilinear predicates, unions of intervals, or intervals) and on the presence or not of non-determinism.

Subject Classification

ACM Subject Classification
  • Theory of computation → Verification by model checking
Keywords
  • concurrent games
  • parameterized verification

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References

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