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Decidability for Left-Linear Growing Term Rewriting Systems

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Book cover Rewriting Techniques and Applications (RTA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1631))

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Abstract

A term rewriting system is called growing if each variable occurring both the left-hand side and the right-hand side of a rewrite rule occurs at depth zero or one in the left-hand side. Jacquemard showed that the reachability and the sequentiality of linear (i.e., left-right-linear) growing term rewriting systems are decidable. In this paper we show that Jacquemard’s result can be extended to left-linear growing rewriting systems that may have right-non-linear rewrite rules. This implies that the reachability and the joinability of some class of right-linear term rewriting systems are decidable, which improves the results for rightground term rewriting systems by Oyamaguchi. Our result extends the class of left-linear term rewriting systems having a decidable call-by-need normalizing strategy. Moreover, we prove that the termination property is decidable for almost orthogonal growing term rewriting systems.

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Author information

Authors and Affiliations

  1. School of Information Science, JAIST, Tatsunokuchi, Ishikawa, 923-1292, Japan

    Takashi Nagaya & Yoshihito Toyama

Authors
  1. Takashi Nagaya
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  2. Yoshihito Toyama
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany — SUNY, Albany, NY, 12222, USA

    Paliath Narendran

  2. LORIA — INRIA Lorraine 615, rue du Jardin Botanique, F-54602, Villers les Nancy, Cedex, France

    Michael Rusinowitch

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© 1999 Springer-Verlag Berlin Heidelberg

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Nagaya, T., Toyama, Y. (1999). Decidability for Left-Linear Growing Term Rewriting Systems. In: Narendran, P., Rusinowitch, M. (eds) Rewriting Techniques and Applications. RTA 1999. Lecture Notes in Computer Science, vol 1631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48685-2_22

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  • DOI: https://doi.org/10.1007/3-540-48685-2_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66201-3

  • Online ISBN: 978-3-540-48685-5

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