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Recognizing Boolean Closed A-Tree Languages with Membership Conditional Rewriting Mechanism

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Rewriting Techniques and Applications (RTA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2706))

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Abstract

This paper provides an algorithm to compute the complement of tree languages recognizable with A-TA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizability of A-closures of regular tree languages. In the proof of the main result, a new framework of tree automata, called sequence-tree automata, is introduced as a generalization of Lugiez and Dal Zilio’s multi-tree automata [14] of an associativity case. It is also shown that recognizable A-tree languages are closed under a one-step rewrite relation in case of ground A-term rewriting. This result allows us to compute an under-approximation of A-rewrite descendants of recognizable A-tree languages with arbitrary accuracy.

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Author information

Authors and Affiliations

  1. PRESTO “Information and Systems”, Japan Science and Technology Corporation, Japan

    Hitoshi Ohsaki

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

    Hitoshi Ohsaki & Toshinori Takai

  3. Nara Institute of Science and Technology, Takayama 8916-5, Ikoma, 630-0192, Japan

    Hiroyuki Seki

Authors
  1. Hitoshi Ohsaki
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  2. Hiroyuki Seki
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  3. Toshinori Takai
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Editor information

Editors and Affiliations

  1. Dpt. Lenguajes y Sistemas Informáticos (LSI), Technical University of Catalonia (UPC), Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

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Ohsaki, H., Seki, H., Takai, T. (2003). Recognizing Boolean Closed A-Tree Languages with Membership Conditional Rewriting Mechanism. In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_34

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  • DOI: https://doi.org/10.1007/3-540-44881-0_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40254-1

  • Online ISBN: 978-3-540-44881-5

  • eBook Packages: Springer Book Archive

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