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Symbolic Approximation of Weighted Timed Games

Authors Damien Busatto-Gaston, Benjamin Monmege , Pierre-Alain Reynier



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Author Details

Damien Busatto-Gaston
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
Benjamin Monmege
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
Pierre-Alain Reynier
  • Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France

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Damien Busatto-Gaston, Benjamin Monmege, and Pierre-Alain Reynier. Symbolic Approximation of Weighted Timed Games. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 28:1-28:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2018.28

Abstract

Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the accumulated weight while reaching a target. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. For non-negative weights, the largest class that can be analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the value problem is undecidable, the authors show how to approximate the value by considering regions with a refined granularity. In this work, we extend this class to incorporate negative weights, allowing one to model energy for instance, and prove that the value can still be approximated, with the same complexity. In addition, we show that a symbolic algorithm, relying on the paradigm of value iteration, can be used as an approximation schema on this class.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Timed and hybrid models
  • Theory of computation → Quantitative automata
Keywords
  • Weighted timed games
  • Real-time systems
  • Game theory
  • Approximation

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References

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