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Games with Winning Conditions of High Borel Complexity

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

We first consider infinite two-player games on pushdown graphs. In previous work, Cachat, Duparc and Thomas [4] have presented a winning decidable condition that is Σ3-complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We extend this result by giving a family of decidable winning conditions of arbitrary high finite Borel complexity. From this family, we deduce a family of decidable winning conditions of arbitrary finite Borel complexity for games played on finite graphs. The problem of deciding the winner for these winning conditions is shown to be non-elementary complete.

This research has been partially supported by the European Community Research Training Network “Games and Automata for Synthesis and Validation” (GAMES), (contract HPRN-CT-2002-00283), see www.games.rwth-aachen.de.

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Author information

Authors and Affiliations

  1. LIAFA, Université Paris VII, 2, place Jussieu, case 7014, F-75251, Paris Cedex 05

    Olivier Serre

Authors
  1. Olivier Serre
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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Serre, O. (2004). Games with Winning Conditions of High Borel Complexity. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_95

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_95

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

  • eBook Packages: Springer Book Archive

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