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Monotone AC-Tree Automata

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3835))

Abstract

We consider several questions about monotone AC-tree automata, a class of equational tree automata whose transition rules correspond to rules in Kuroda normal form of context-sensitive grammars. Whereas it has been proved that this class has a decision procedure to determine if, given a monotone AC-tree automaton, it accepts no terms, other important decidability or complexity results have not been well-investigated yet. In the paper, we prove that the membership problem for monotone AC-tree automata is PSPACE-complete. We then study the expressiveness of monotone AC-tree automata: precisely, we prove that the family of AC-regular tree languages is strictly subsumed in that of AC-monotone tree languages. The proof technique used in obtaining the above result yields the answers to two different questions, specifically that the family of monotone AC-tree languages is not closed under complementation, and that the inclusion problem for monotone AC-tree automata is undecidable.

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Author information

Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology, PRESTO, Japan Science and Technology Agency,  

    Hitoshi Ohsaki

  2. Laboratoire d’Informatique Fondamentale de Lille, Université des Sciences et Technologies de Lille, France

    Jean-Marc Talbot, Sophie Tison & Yves Roos

Authors
  1. Hitoshi Ohsaki
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  2. Jean-Marc Talbot
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  3. Sophie Tison
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  4. Yves Roos
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Editor information

Editors and Affiliations

  1. University of Miami, USA

    Geoff Sutcliffe

  2. University of Manchester, UK

    Andrei Voronkov

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© 2005 Springer-Verlag Berlin Heidelberg

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Ohsaki, H., Talbot, JM., Tison, S., Roos, Y. (2005). Monotone AC-Tree Automata. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_24

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  • DOI: https://doi.org/10.1007/11591191_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30553-8

  • Online ISBN: 978-3-540-31650-3

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