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The Algebraic Counterpart of the Wagner Hierarchy

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Logic and Theory of Algorithms (CiE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

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Abstract

The algebraic study of formal languages shows that ω-rational languages are exactly the sets recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context.

More precisely, we first define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a decidable and well-founded partial ordering of width 2 and height ω ω.

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Authors and Affiliations

  1. Faculty of Business and Economics HEC, Institute of Information Systems ISI, Université de Lausanne, CH-1015, Lausanne, Switzerland

    Jérémie Cabessa & Jacques Duparc

Authors
  1. Jérémie Cabessa
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  2. Jacques Duparc
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Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

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Cabessa, J., Duparc, J. (2008). The Algebraic Counterpart of the Wagner Hierarchy. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_11

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  • DOI: https://doi.org/10.1007/978-3-540-69407-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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