Reachability Switching Games

Authors John Fearnley, Martin Gairing, Matthias Mnich, Rahul Savani

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John Fearnley
  • University of Liverpool, UK
Martin Gairing
  • University of Liverpool, UK
Matthias Mnich
  • Universität Bonn, Germany , and Maastricht University, The Netherlands
Rahul Savani
  • University of Liverpool, UK

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John Fearnley, Martin Gairing, Matthias Mnich, and Rahul Savani. Reachability Switching Games. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 124:1-124:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In this paper, we study the problem of deciding the winner of reachability switching games. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP n coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. We also study the structure of winning strategies in these games, and in particular we show that exponential memory is required in both the one- and two-player settings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Deterministic Random Walks
  • Model Checking
  • Reachability
  • Simple Stochastic Game
  • Switching Systems


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