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On Rational Trees

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Computer Science Logic (CSL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4207))

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Abstract

Rational graphs are a family of graphs defined using labelled rational transducers. Unlike automatic graphs (defined using synchronized transducers) the first order theory of these graphs is undecidable, there is even a rational graph with an undecidable first order theory. In this paper we consider the family of rational trees, that is rational graphs which are trees. We prove that first order theory is decidable for this family. We also present counter examples showing that this result cannot be significantly extended both in terms of logic and of structure.

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Author information

Authors and Affiliations

  1. IRISA, Campus de Beaulieu, 35042, Rennes, France

    Arnaud Carayol & Christophe Morvan

Authors
  1. Arnaud Carayol
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  2. Christophe Morvan
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Zoltán Ésik

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© 2006 Springer-Verlag Berlin Heidelberg

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Carayol, A., Morvan, C. (2006). On Rational Trees. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_15

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  • DOI: https://doi.org/10.1007/11874683_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45458-8

  • Online ISBN: 978-3-540-45459-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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