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Divergence phenomena during completion

  • Andrea Sattler-Klein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Andrea Sattler-Klein
    • 1
  1. 1.Fachbereich InformatikUniversität KaiserslauternKaiserslauternFRG

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