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Processes, Terms and Cycles: Steps on the Road to Infinity pp 127–147Cite as

Primitive Rewriting

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 3838)

Abstract

Undecidability results in rewriting have usually been proved by reduction from undecidable problems of Turing machines or, more recently, from Post’s Correspondence Problem. Another natural candidate for proofs regarding term rewriting is Recursion Theory, a direction we promote in this contribution.

We present some undecidability results for “primitive” term rewriting systems, which encode primitive-recursive definitions, in the manner suggested by Klop. We also reprove some undecidability results for orthogonal and non-orthogonal rewriting by applying standard results in recursion theory.

Keywords

  • Normal Form
  • Turing Machine
  • Recursive Function
  • Critical Pair
  • Recursion Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported by the Israel Science Foundation (grant no. 250/05).

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Ramat Aviv, 69978, Israel

    Nachum Dershowitz

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  1. Nachum Dershowitz
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Editors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Aart Middeldorp

  2. Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS, Utrecht, The Netherlands

    Vincent van Oostrom

  3. Department of Theoretical Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Femke van Raamsdonk

  4. VU Vrije Universiteit Amsterdam,  

    Roel de Vrijer

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Dershowitz, N. (2005). Primitive Rewriting. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_10

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  • DOI: https://doi.org/10.1007/11601548_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30911-6

  • Online ISBN: 978-3-540-32425-6

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