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A polynomial time algorithm for finding finite unions of tree pattern languages

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Nonmonotonic and Inductive Logic (NIL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 659))

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Abstract

A tree pattern is a structured pattern known as a term in formal logic, and a tree pattern language is the set of trees which are the ground instances of a tree pattern. In this paper, we deal with the class of tree languages whose language is defined as a union of at most k tree pattern languages, where k is an arbitrary fixed positive number. In particular, We present a polynomial time algorithm that, given a finite set of trees, to find a set of tree patterns that defines a minimal union of at most k tree pattern languages containing the given set. The algorithm can be considered as a natural extension of Plotkin's anti-unification algorithm, which finds a minimal single tree pattern language containing the given set. By using the algorithm, we can realize a consistent and conservative polynomial time inference machine that identifies the class of unions of k tree pattern languages in the limit from positive data for every k > 0.

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Authors and Affiliations

  1. Department of Artificial Intelligence, Kyushu Institute of Technology, 680-4, Kawazu, 820, Iizuka, Japan

    Hiroki Arimura, Takeshi Shinohara & Setsuko Otsuki

Authors
  1. Hiroki Arimura
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  2. Takeshi Shinohara
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  3. Setsuko Otsuki
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Editor information

Gerhard Brewka Klaus P. Jantke Peter H. Schmitt

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© 1993 Springer-Verlag Berlin Heidelberg

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Arimura, H., Shinohara, T., Otsuki, S. (1993). A polynomial time algorithm for finding finite unions of tree pattern languages. In: Brewka, G., Jantke, K.P., Schmitt, P.H. (eds) Nonmonotonic and Inductive Logic. NIL 1991. Lecture Notes in Computer Science, vol 659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030389

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  • DOI: https://doi.org/10.1007/BFb0030389

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56433-1

  • Online ISBN: 978-3-540-47557-6

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