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Logics and Automata for Totally Ordered Trees

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Rewriting Techniques and Applications (RTA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5117))

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Abstract

A totally ordered tree is a tree equipped with an additional total order on its nodes. It provides a formal model for data that comes with both a hierarchical and a sequential structure; one example for such data are natural language sentences, where a sequential structure is given by word order, and a hierarchical structure is given by grammatical relations between words. In this paper, we study monadic second-order logic (MSO) for totally ordered terms. We show that the MSO satisfiability problem of unrestricted structures is undecidable, but give a decision procedure for practically relevant sub-classes, based on tree automata.

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Author information

Authors and Affiliations

  1. Uppsala University, Sweden

    Marco Kuhlmann

  2. INRIA, Lille, France

    Joachim Niehren

Authors
  1. Marco Kuhlmann
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  2. Joachim Niehren
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Andrei Voronkov

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© 2008 Springer-Verlag Berlin Heidelberg

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Kuhlmann, M., Niehren, J. (2008). Logics and Automata for Totally Ordered Trees. In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_15

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  • DOI: https://doi.org/10.1007/978-3-540-70590-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70588-8

  • Online ISBN: 978-3-540-70590-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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