Skip to main content
Springer Nature Link
Log in

Complete equational unification based on an extension of the Knuth-Bendix completion procedure

  • Conference paper
  • First Online:
Word Equations and Related Topics (IWWERT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 572))

Included in the following conference series:

  • 130 Accesses

Abstract

A unifier is a substitution that makes two terms syntactically equal. In this paper, we discuss a more semantical unifier: an equational unifier, which is a substitution that makes two terms equal modulo a congruence relation. As a result we will give a general procedure that enumerates a complete set of equational unifiers for a given pair of terms under a given congruence.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bachmair, L., Dershowitz, N., and Hsiang, J.: Ordering for equational proof, Proc. Symp. Logic in Computer Science, Cambridge, Massachusetts (June 1986)

    Google Scholar 

  2. Bachmair, L., Dershowitz, N., and Plaisted, D. A.: Completion without failure, Proc. Colloquium on Resolution of Equations in Algebraic Structures (1987)

    Google Scholar 

  3. Bosco, P. G., Giovannetti, F., and Moiso, C.: Refined strategies for equational proofs, TAPSOFT '87, LNCS 250, pp. 276–290 (1987)

    Google Scholar 

  4. Dershowitz, N. and Manna, Z.: Proving termination with multiset orderings, Comm. ACM 22, pp. 465–467 (1979)

    Google Scholar 

  5. Dershowitz, N.: Orderings for term-rewriting systems, Theoretical Computer Science 17, pp. 279–301 (1982)

    Google Scholar 

  6. Fages, F.: Associative-commutative unification, 7th International Conference on Automated Deduction, LNCS 170, pp. 194–208 (1984)

    Google Scholar 

  7. Fages, F. and Huet, G.: Complete sets of unifiers and matchers in equational theories, Theoretical Computer Science 43, pp. 189–200 (1986)

    Google Scholar 

  8. Fay, M.: First order unification in an equational theory, 4th workshop on Automated Deduction, Austin, Texas, pp. 161–167 (1979)

    Google Scholar 

  9. Gallier, J. H. and Snyder, W.: A general complete E-unification procedure, Rewriting Techniques and Applications, LNCS 256, pp. 216–227 (1987)

    Google Scholar 

  10. Hsiang, J.: Rewrite method for theorem proving in first order theory with equality, J. Symbolic Computation, 3, 133–151 (1987)

    Google Scholar 

  11. Huet, G.: An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations, Inform. Process. Lett. 7, pp. 144–147 (1978)

    Google Scholar 

  12. Huet, G. and Oppen, D. C.: Equations and Rewrite Rules: a survey, Formal Language: Perspectives and Open Problems Academic Press, pp. 349–405 (1980)

    Google Scholar 

  13. Huet, G.: A complete proof of correctness of the Knuth-Bendix completion algorithm, J. Computer and System Science 23, pp. 11–21 (1981)

    Google Scholar 

  14. Hullot, J. M.: Canonical forms and unification, 5th Workshop on Automated Deduction, LNCS 87, pp. 318–334 (1980)

    Google Scholar 

  15. Knuth, D. E. and Bendix, P. B.: Simple word problems in universal algebras, Computational problems in abstract algebra, Pergamon Press, Oxford (1970)

    Google Scholar 

  16. Makanin, G. S.: The problem of solvability of equations in a free semigroup, Soviet Akad. Nauk SSSR, Tom 233, No. 2 (1977)

    Google Scholar 

  17. Robinson, J. A.: A machine-oriented logic based on the resolution principle, J. ACM 12, pp. 23–41 (1965)

    Google Scholar 

  18. Rusinowitch, M.: Theorem-proving with resolution and superposition: an extension of the Knuth and Bendix procedure to acomplete set of inference rules, International Conference on Fifth Generation Computer Systems, 1988, pp. 524–531 (1988)

    Google Scholar 

  19. Sakai, K.: An ordering method for term rewriting systems, Technical Report 062, ICOT (1984)

    Google Scholar 

  20. Siekmann, J. H.: Unification theory, J. Symbolic Computation 7, pp. 207–274 (1989)

    Google Scholar 

  21. Smullyan, R. M.: To Mock a Mockingbird, Alfred A. Knopf, Inc. (1985)

    Google Scholar 

  22. Stickel, M.E.: A unification algorithm for associative-commutative functions, J. ACM, 28, 3, pp. 423–434 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Toshiba Corporation, 70 Yanagicho, Saiwai-ku, 210, Kawasaki-shi, Japan

    Akihiko Ohsuga

  2. ICOT Research Center, 1-4-28, Mita Minato-ku, 108, Tokyo, Japan

    Kô Sakai

Authors
  1. Akihiko Ohsuga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kô Sakai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

K. U. Schulz

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohsuga, A., Sakai, K. (1992). Complete equational unification based on an extension of the Knuth-Bendix completion procedure. In: Schulz, K.U. (eds) Word Equations and Related Topics. IWWERT 1990. Lecture Notes in Computer Science, vol 572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55124-7_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-55124-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55124-9

  • Online ISBN: 978-3-540-46737-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation