Relative undecidability in term rewriting: II. the confluence hierarchy

  • Authors:

  • Alfons Geser;Aart Middeldorp;Enno Ohlebusch;Hans Zantema

  • Affiliations:

  • ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, Virginia;Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Japan;Faculty of Technology, University of Bielefeld, P.O. Box 10 01 31, 33501 Bielefeld, Germany;Department of Computing Science, Eindhoven University of Technology, P.O. Box 513, MB Eindhoven, The Netherlands

  • Venue:
  • Information and Computation
  • Year:
  • 2002

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Abstract

For a hierarchy of properties of term rewriting systems related to confluence we prove relative undecidability, i.e., for implications X ↠ Y in the hierarchy the property X is undecidable for term rewriting systems satisfying Y. For some of the implications either X or -X is semi-decidable, for others neither X nor -X is semi-decidable. We prove most of these results for linear term rewrite systems.