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The first-order theory of one step rewriting in linear noetherian systems is undecidable

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Rewriting Techniques and Applications (RTA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1232))

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Abstract

We construct a finite linear finitely terminating rewrite rule system with undecidable theory of one step rewriting.

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References

  1. W. V. Quine. Concatenation as a basis for arithmetic. J. Symb. Logic, 11(4):105–114, 1946.

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  2. R. Treinen. The first-order theory of one step rewriting is undecidable. In Rewriting Techniques and Applications'96, Lect. Notes Comput. Sci., pages 276–285. Springer-Verlag, 1996.

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  3. S. Vorobyov. The elementary theory of one-step rewriting is undecidable (note). Unpublished draft, see http://www.mpi-sb.mpg/∼sv/, Section “On Trees and Rewriting”, 1995.

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  4. S. Vorobyov. ∃∀∃-theories of one step rewriting in linear noetherian systems are undecidable. Available at http://www.mpi-sb.mpg.de/∼sv, November 1996.

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Sergei Vorobyov

Authors
  1. Sergei Vorobyov
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Hubert Comon

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© 1997 Springer-Verlag Berlin Heidelberg

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Vorobyov, S. (1997). The first-order theory of one step rewriting in linear noetherian systems is undecidable. In: Comon, H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62950-5_76

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  • DOI: https://doi.org/10.1007/3-540-62950-5_76

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62950-4

  • Online ISBN: 978-3-540-69051-1

  • eBook Packages: Springer Book Archive

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