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On nontermination of Knuth-Bendix algorithm

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Book cover Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

The well-known Knuth-Bendix completion algorithm which computes a confluent and finitely terminating term rewriting system from a given set of equations, can either terminate with success or abort or even nonterminate. Very little is known about the origin of nontermination of this algorithm. We study the structural properties of rewrite rules which cause nontermination. The notion of the crossed rules is introduced for these purposes. We look for sufficient conditions guaranteeing nontermination of algorithm in the presence of crossed rules. A special attention is devoted to a verifiable condition of such kind.

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References

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Authors and Affiliations

  1. VUSEI-AR, CS, 842 21, Bratislava, Czechoslovakia

    Mikuláš Hermann & Igor Prívara

Authors
  1. Mikuláš Hermann
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  2. Igor Prívara
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Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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Hermann, M., Prívara, I. (1986). On nontermination of Knuth-Bendix algorithm. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_64

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  • DOI: https://doi.org/10.1007/3-540-16761-7_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

  • eBook Packages: Springer Book Archive

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