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Algebras, Automata and Logic for Languages of Labeled Birooted Trees

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7966))

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Abstract

In this paper, we study the languages of labeled finite birooted trees: Munn’s birooted trees extended with vertex labeling. We define a notion of finite state birooted tree automata that is shown to capture the class of languages that are upward closed w.r.t. the natural order and definable in Monadic Second Order Logic. Then, relying on the inverse monoid structure of labeled birooted trees, we derive a notion of recognizable languages by means of (adequate) premorphisms into finite (adequately) ordered monoids. This notion is shown to capture finite boolean combinations of languages as above. We also provide a simple encoding of finite (mono-rooted) labeled trees in an antichain of labeled birooted trees that shows that classical regular languages of finite (mono-rooted) trees are also recognized by such premorphisms and finite ordered monoids.

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Author information

Authors and Affiliations

  1. LaBRI UMR 5800, Université de Bordeaux, 351, cours de la Libération, F-33405, Talence, France

    David Janin

Authors
  1. David Janin
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, Wolfson Building, Parks Road, University of Oxford, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Janin, D. (2013). Algebras, Automata and Logic for Languages of Labeled Birooted Trees. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_29

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  • DOI: https://doi.org/10.1007/978-3-642-39212-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39211-5

  • Online ISBN: 978-3-642-39212-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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