English

On the Parameterized Complexity of Associative and Commutative Unification

Symbolic Computation 2013-10-04 v1

Abstract

This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and associative-commutative unification problems are W[1]W[1]-hard. A fixed-parameter algorithm and a polynomial-time algorithm are presented for special cases of commutative unification in which one input term is variable-free and the number of variables is bounded by a constant, respectively. Related results including those on the string and tree edit distance problems with variables are shown too.

Keywords

Cite

@article{arxiv.1310.0919,
  title  = {On the Parameterized Complexity of Associative and Commutative Unification},
  author = {Tatsuya Akutsu and Takeyuki Tamura and Atsuhiro Takasu},
  journal= {arXiv preprint arXiv:1310.0919},
  year   = {2013}
}
R2 v1 2026-06-22T01:39:32.427Z