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On Reachability Games of Ordinal Length

  • Conference paper
SOFSEM 2008: Theory and Practice of Computer Science (SOFSEM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4910))

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Abstract

Games are a classical model in the synthesis of controllers in the open setting. In particular, games of infinite length can represent systems which are not expected to reach a correct state, but rather to handle a continuous stream of events. Yet, even longer sequences of events have to be considered when infinite sequences of events can occur in finite time — Zeno behaviours.

In this paper, we extend two-player games to this setting by considering plays of ordinal length. Our two main results are determinacy of reachability games of length less than ω ω on finite arenas, and the PSPACE-completeness of deciding the winner in such a game.

This paper was supported in part by the French ANR DOTS.

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Authors and Affiliations

  1. LIAFA, Université Paris 7, Case 7014, 2 place Jussieu, F-75251, Paris 5, France

    Julien Cristau & Florian Horn

  2. Lehrstuhl für Informatik VII, RWTH, Ahornstraße 55, 52056, Aachen, Germany

    Florian Horn

Authors
  1. Julien Cristau
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  2. Florian Horn
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Editor information

Viliam Geffert Juhani Karhumäki Alberto Bertoni Bart Preneel Pavol Návrat Mária Bieliková

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Cristau, J., Horn, F. (2008). On Reachability Games of Ordinal Length. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds) SOFSEM 2008: Theory and Practice of Computer Science. SOFSEM 2008. Lecture Notes in Computer Science, vol 4910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77566-9_18

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  • DOI: https://doi.org/10.1007/978-3-540-77566-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77565-2

  • Online ISBN: 978-3-540-77566-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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