1. On the parameterized complexity of associative and commutative unification.
- Author
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Akutsu, Tatsuya, Jansson, Jesper, Takasu, Atsuhiro, and Tamura, Takeyuki
- Subjects
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COMPUTATIONAL complexity , *COMPUTER algorithms , *DYNAMIC programming , *GRAPH theory , *MATHEMATICAL variables - Abstract
This article studies the parameterized complexity of the unification problem with associative, commutative, or associative-commutative functions with respect to the parameter “number of variables”. It is shown that if every variable occurs only once then both of the associative and associative-commutative unification problems can be solved in polynomial time, but that in the general case, both problems are W [ 1 ] -hard even when one of the two input terms is variable-free. For commutative unification, an algorithm whose time complexity depends exponentially on the number of variables is presented; moreover, if a certain conjecture is true then the special case where one input term is variable-free belongs to FPT. Some related results are also derived for a natural generalization of the classic string and tree edit distance problems that allows variables. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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