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Decidability and Closure Properties of Equational Tree Languages

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Rewriting Techniques and Applications (RTA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

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Abstract

Equational tree automata provide a powerful tree language framework that facilitates to recognize congruence closures of tree languages. In the paper we show the emptiness problem for AC-tree automata and the intersection-emptiness problem for regular AC-tree automata, each of which was open in our previous work [20], are decidable, by a straightforward reduction to the reachability problem for ground AC-term rewriting. The newly obtained results generalize decidability of so-called reachable property problem of Mayr and Rusinowitch [17]. We then discuss complexity issue of AC-tree automata. Moreover, in order to solve some other questions about regular A- and AC-tree automata, we recall the basic connection between word languages and tree languages.

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Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology, Nakoji 3-11-46, Amagasaki, 661-0974, Japan

    Hitoshi Ohsaki & Toshinori Takai

Authors
  1. Hitoshi Ohsaki
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  2. Toshinori Takai
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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© 2002 Springer-Verlag Berlin Heidelberg

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Ohsaki, H., Takai, T. (2002). Decidability and Closure Properties of Equational Tree Languages. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_9

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  • DOI: https://doi.org/10.1007/3-540-45610-4_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

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