An Algorithm for General Set Unification and Its Complexity

Authors:
Frieder Stolzenburg
Affiliations:
Univ. Koblenz, Institut f. Informatik, Rheinau 1, D–56075 Koblenz, Germany. e-mail: stolzen@informatik.uni-koblenz.de
Venue:
Journal of Automated Reasoning
Year:
1999

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Abstract

In this paper, an algorithm for set unification – which is arestricted case of the associative-commutative-idempotent (ACI) unification– is presented. The algorithm is able to unify finite sets containingarbitrary terms. It is nondeterministic and can easily be implemented inProlog. Because of the simplicity of the algorithm, the computation of asingle solution is quite fast, and the exact complexity of the algorithm andof the set unification problem itself can be analyzed easily. The algorithmis compared with some other set unification algorithms. All algorithms havesingle exponential complexity, because the set unification problem isNP-complete, but our exact complexity analysis provides more details. It isshown how the algorithm presented here can be used to solve a generalizedset unification problem where sets with tails are admissible. The algorithmcan be used in any logic programming language embedding (finite) sets, or inother contexts where set unification is needed, for example, in someunification-based grammar formalisms.