NP-completeness of the set unification and matching problems

  • Deepak Kapur
  • Paliath Narendran
Unification Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


The set-unification and set-matching problems, which are very restricted cases of the associative-commutative-idempotent unification and matching problems, respectively, are shown to be NP-complete. The NP-completeness of the subsumption check in first-order resolution follows from these results. It is also shown that commutative-idempotent matching and associative-idempotent matching are NP-hard, thus implying that the idempotency of a function does not help in reducing the complexity of matching and unification problems.


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6. References

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    Benanav, D., Kapur, D., and Narendran, P., ”Complexity of Matching Problems,” Proc. of the First International Conf on Rewrite Techniques and Applications, Dijon, France, May 1985.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Deepak Kapur
    • 1
  • Paliath Narendran
    • 1
  1. 1.Corporate Research and Development General Electric CompanyComputer Science BranchSchenectady

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