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Parametrized Regular Infinite Games and Higher-Order Pushdown Strategies

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Fundamentals of Computation Theory (FCT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5699))

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Abstract

Given a set P of natural numbers, we consider infinite games where the winning condition is a regular ω-language parametrized by P. In this context, an ω-word, representing a play, has letters consisting of three components: The first is a bit indicating membership of the current position in P, and the other two components are the letters contributed by the two players. Extending recent work of Rabinovich we study here predicates P where the structure (ℕ, + 1, P) belongs to the pushdown hierarchy (or “Caucal hierarchy”). For such a predicate P where (ℕ, + 1, P) occurs in the k-th level of the hierarchy, we provide an effective determinacy result and show that winning strategies can be implemented by deterministic level-k pushdown automata.

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Authors and Affiliations

  1. Lehrstuhl Informatik 7, RWTH Aachen University, Aachen, Germany

    Paul Hänsch, Michaela Slaats & Wolfgang Thomas

Authors
  1. Paul Hänsch
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  2. Michaela Slaats
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  3. Wolfgang Thomas
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Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski  & Maciej Gębala  & 

  2. Institute of Computer Science, University of Wrocław, ul. Joliot-Curie 15, 50-383, Wrocław, Poland

    Witold Charatonik

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Hänsch, P., Slaats, M., Thomas, W. (2009). Parametrized Regular Infinite Games and Higher-Order Pushdown Strategies. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds) Fundamentals of Computation Theory. FCT 2009. Lecture Notes in Computer Science, vol 5699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03409-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-03409-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03408-4

  • Online ISBN: 978-3-642-03409-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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