On the Parameterized Complexity of Associative and Commutative Unification

  • Tatsuya AkutsuEmail author
  • Jesper Jansson
  • Atsuhiro Takasu
  • Takeyuki Tamura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)


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.


Function Symbol Edit Distance Edit Operation Input Term Unification Problem 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tatsuya Akutsu
    • 1
    Email author
  • Jesper Jansson
    • 1
    • 2
  • Atsuhiro Takasu
    • 3
  • Takeyuki Tamura
    • 1
  1. 1.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityKyotoJapan
  2. 2.The Hakubi ProjectKyoto UniversityKyotoJapan
  3. 3.National Institute of InformaticsTokyoJapan

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