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On the Parameterized Complexity of Associative and Commutative Unification

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Parameterized and Exact Computation (IPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8894))

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Abstract

This paper studies the unification problem with associative, commutative, and associative-commutative functions. The parameterized complexity is analyzed with respect to the parameter “number of variables”. It is shown that both the associative and associative-commutative unification problems are \(W[1]\)-hard. For commutative unification, a polynomial-time algorithm is presented in which the number of variables is assumed to be a constant. Some related results for the string and tree edit distance problems with variables are also presented.

This work was partially supported by the Collaborative Research Programs of National Institute of Informatics.

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Notes

  1. 1.

    In the literature, “replacement” is usually referred to as “substitution”. Here, we use “replacement” to distinguish it from the “substitution” of variables defined above.

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Author information

Authors and Affiliations

  1. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

    Tatsuya Akutsu, Jesper Jansson & Takeyuki Tamura

  2. The Hakubi Project, Kyoto University, Sakyo-ku, Kyoto, 606-8501, Japan

    Jesper Jansson

  3. National Institute of Informatics, Tokyo, 101-8430, Japan

    Atsuhiro Takasu

Authors
  1. Tatsuya Akutsu
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  2. Jesper Jansson
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  3. Atsuhiro Takasu
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  4. Takeyuki Tamura
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Corresponding author

Correspondence to Tatsuya Akutsu .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan

  2. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Akutsu, T., Jansson, J., Takasu, A., Tamura, T. (2014). On the Parameterized Complexity of Associative and Commutative Unification. In: Cygan, M., Heggernes, P. (eds) Parameterized and Exact Computation. IPEC 2014. Lecture Notes in Computer Science(), vol 8894. Springer, Cham. https://doi.org/10.1007/978-3-319-13524-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-13524-3_2

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