Complexity of matching problems

Abstract

We show that the associative-commutative matching problem is NP-complete; more precisely, the matching problem for terms in which some function symbols are uninterpreted and others are both associative and commutative, is NP-complete. It turns out that the similar problems of associative-matching and commutative-matching are also NP-complete. However, if every variable appears at most once in a term being matched, then the associative-commutative matching problem is shown to have an upper-bound of O (|s| * |t|3), where |s| and |t| are respectively the sizes of the pattern s and the subject t.