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A theorem-proving approach to the Knuth-Bendix completion algorithm

  • 3. Abstract Data Types And Revrite Rules
  • Conference paper
  • First Online:
Computer Algebra (EUROCAM 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 144))

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Abstract

The process of algebraic abstract data type completion has some similarities with resolution theorem-proving. In particular, some proof strategies developed in the field of computational logic are applicable to the Knuth-Bendix algorithm as completion strategies. Computational experiments confirm that these heuristics can indeed be employed to control, and limit, the generation of new rules during the completion process.

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References

  1. Huet G.: Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Journ. ACM, Vol 27, No 4, October 1980.

    Google Scholar 

  2. Huet G.: A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm. Rapport de Recherche No 25, INRIA Le Chesnay, 1980.

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  3. Huet G., Oppen D.C.: Equations and Rewrite Rules: a Survey. Techn. Report CSL-111, SRI international, January 1980.

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  4. Knuth D.E., Bendix P.B.: Simple Word Problems in Universal Algebras. In: "Computational Problems in Abstract Algebra", Ed. Leech J., Pergamon, Oxford 1970, pp 263–297.

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  5. Loos R.G.K: The Algorithm Description Language ALDES (Report). SIGSAM Bulletin of the ACM, Vol 10 Nr 1, Febr 1976.

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  6. Nilsson N.J.: Problem Solving Methods in Artificial Intelligence. McGraw Hill 1971.

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  7. Robinson J.A.: A Machine Oriented Logic Based on the Resolution Principle. Journ. ACM Vol 12 No 1, January 1965.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik I, Universität Karlsruhe, Postfach 6380, D-7500, Karlsruhe 1

    Wolfgang Küchlin

Authors
  1. Wolfgang Küchlin
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Editor information

Jacques Calmet

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© 1982 Springer-Verlag Berlin Heidelberg

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Küchlin, W. (1982). A theorem-proving approach to the Knuth-Bendix completion algorithm. In: Calmet, J. (eds) Computer Algebra. EUROCAM 1982. Lecture Notes in Computer Science, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11607-9_12

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  • DOI: https://doi.org/10.1007/3-540-11607-9_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11607-3

  • Online ISBN: 978-3-540-39433-4

  • eBook Packages: Springer Book Archive

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