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Divergence phenomena during completion

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Rewriting Techniques and Applications (RTA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 488))

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Abstract

We will show how any primitive recursive function may be encoded in a finite canonical string rewriting system. Using these encodings for every primitive recursive function f (and even for every recursively enumerable set ©) a finite string rewriting system ℜ and a noetherian ordering > may be constructed such that completion of ℜ with respect to > will generate a divergence sequence that encodes explicitly the input/output behaviour of f (or the set ©, respectively). Furthermore, we will show by an example that if completion of a set ℜ with respect to a noetherian ordering > diverges, then there need not exist any rule that causes infinitely many other ones by overlapping.

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Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, FRG

    Andrea Sattler-Klein

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  1. Andrea Sattler-Klein
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Ronald V. Book

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© 1991 Springer-Verlag Berlin Heidelberg

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Sattler-Klein, A. (1991). Divergence phenomena during completion. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_111

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  • DOI: https://doi.org/10.1007/3-540-53904-2_111

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53904-9

  • Online ISBN: 978-3-540-46383-2

  • eBook Packages: Springer Book Archive

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