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A Kleene Theorem for Weighted Tree Automata over Tree Valuation Monoids

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

Cauchy unital tree valuation monoids are introduced as weight structures for weighted tree automata. Rational tree series over this kind of monoids are defined and Kleene’s classical theorem is proved for this setting: a tree series over a Cauchy unital tree valuation monoid is recognizable if and only if it is rational.

Supported by the German Academic Exchange Service (DAAD) and the Hungarian Scholarship Board Office (MÖB) project “Theory and Applications of Automata” (grant 5567). The second and the third author were partially supported by the NKFI grant no. K 108448 and by the DFG Graduiertenkolleg 1763 (QuantLA), respectively.

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Notes

  1. 1.

    We are thankful to an anonymous referee for spotting a mistake in a previous version of this example.

  2. 2.

    Here \(\sum \) denotes the ordinary sum of numbers with the natural extension to \(-\infty \).

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, 04109, Leipzig, Germany

    Manfred Droste & Doreen Götze

  2. Institute of Informatics, University of Szeged, Szeged, 6701, Hungary

    Zoltán Fülöp

Authors
  1. Manfred Droste
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  2. Zoltán Fülöp
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  3. Doreen Götze
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Corresponding author

Correspondence to Doreen Götze .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Droste, M., Fülöp, Z., Götze, D. (2016). A Kleene Theorem for Weighted Tree Automata over Tree Valuation Monoids. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_35

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_35

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-30000-9

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