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Verifying Orientability of Rewrite Rules Using the Knuth-Bendix Order

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Rewriting Techniques and Applications (RTA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2051))

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Abstract

We consider two decision problems related to the Knuth-Bendix order (KBO). The first problem is orientability: given a system of rewrite rules R, does there exist some KBO which orients every ground instance of every rewrite rule in R. The second problem is whether a given KBO orients a rewrite rule. This problem can also be reformulated as the problem of solving a single ordering constraint for the KBO. We prove that both problems can be solved in polynomial time. The algorithm builds upon an algorithm for solving systems of homogeneous linear inequalities over integers. Also we show that if a system is orientable using a real-valued KBO, then it is also orientable using an integer-valued KBO.

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Author information

Authors and Affiliations

  1. University of Manchester, UK

    Konstantin Korovin & Andrei Voronkov

Authors
  1. Konstantin Korovin
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  2. Andrei Voronkov
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Editor information

Editors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

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© 2001 Springer-Verlag Berlin Heidelberg

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Korovin, K., Voronkov, A. (2001). Verifying Orientability of Rewrite Rules Using the Knuth-Bendix Order. In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_12

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  • DOI: https://doi.org/10.1007/3-540-45127-7_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42117-7

  • Online ISBN: 978-3-540-45127-3

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