Journal of Automated Reasoning

, Volume 9, Issue 2, pp 261–288 | Cite as

Complexity of unification problems with associative-commutative operators

  • Deepak Kapur
  • Paliath Narendran
Article

Abstract

The unification problem for terms containing associative and commutative functions is of importance in theorem provers based on term rewriting and resolution methods as well as in logic programming. The complexity of determining whether two such terms are unifiable was known to be NP-hard. It is proved that the problem is NP-complete by describing a nondeterministic polynomial time algorithm for it. The case where the terms are linear and have no common variables is shown to be in P. The NP-completeness of other similar unification problems, in particular, when a function symbol is also idempotent and/or has a unit (identity), is also discussed. Finally, a table of the complexity of E-matching and E-unification problems is given.

Key words

Unification matching associative commutative idempotent identity unit equational theories set matching complexity word equations NP-complete 

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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Deepak Kapur
    • 1
  • Paliath Narendran
    • 1
  1. 1.Institute of Programming and Logics, Department of Computer ScienceState University of New York at AlbanyAlbanyU.S.A.

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