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NP-completeness of the set unification and matching problems

  • Unification Theory
  • Conference paper
  • First Online:
8th International Conference on Automated Deduction (CADE 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 230))

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Abstract

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.

Partially supported by the National Science Foundation Grant no. DCR-8408461.

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6. References

  1. 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.

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  2. Chang, C.-L., and Lee, R. C.-T., Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.

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  3. Garey, M.R., and Johnson, D.S., Computers and Intractability, W.H. Freeman, 1979.

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  4. Hsiang, J., ”Refutational Theorem Proving Using Term Rewriting Systems,” Artificial Intelligence 25 (3), pp. 255–300, March 1985.

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  5. Kapur, D., and Narendran, P., ”An Equational Approach to Theorem Proving in First-Order Predicate Calculus,” Proc. of the Ninth International Joint Conf. on Artificial Intelligence, Los Angeles, August 1985.

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  6. Paterson, M.S., and Wegman, M., ”Linear Unification,” Journal of Computer and System Sciences 16, pp. 158–167, 1978.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Corporate Research and Development General Electric Company, Computer Science Branch, Schenectady, NY

    Deepak Kapur & Paliath Narendran

Authors
  1. Deepak Kapur
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  2. Paliath Narendran
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Editor information

Jörg H. Siekmann

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© 1986 Springer-Verlag Berlin Heidelberg

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Kapur, D., Narendran, P. (1986). NP-completeness of the set unification and matching problems. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_113

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  • DOI: https://doi.org/10.1007/3-540-16780-3_113

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16780-8

  • Online ISBN: 978-3-540-39861-5

  • eBook Packages: Springer Book Archive

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