Optimal Strategies in Pushdown Reachability Games

Authors Arnaud Carayol, Matthew Hague

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Author Details

Arnaud Carayol
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, France
Matthew Hague
  • Royal Holloway, University of London, UK

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Arnaud Carayol and Matthew Hague. Optimal Strategies in Pushdown Reachability Games. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


An algorithm for computing optimal strategies in pushdown reachability games was given by Cachat. We show that the information tracked by this algorithm is too coarse and the strategies constructed are not necessarily optimal. We then show that the algorithm can be refined to recover optimality. Through a further non-trivial argument the refined algorithm can be run in 2EXPTIME by bounding the play-lengths tracked to those that are at most doubly exponential. This is optimal in the sense that there exists a game for which the optimal strategy requires a doubly exponential number of moves to reach a target configuration.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Pushdown Systems
  • Reachability Games
  • Optimal Strategies
  • Formal Methods
  • Context Free


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