Decidability for left-linear growing term rewriting systems

Takashi Nagaya, Yoshihito Toyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationRewriting Techniques and Applications - 10th International Conference, RTA 1999, Proceedings
EditorsPaliath Narendran, Michael Rusinowitch
PublisherSpringer Verlag
Pages256-270
Number of pages15
ISBN (Print)3540662014, 9783540662013
DOIs
Publication statusPublished - 1999 Jan 1
Event10th International Conference on Rewriting Techniques and Applications, RTA 1999 - Trento, Italy
Duration: 1999 Jul 21999 Jul 4

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1631
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on Rewriting Techniques and Applications, RTA 1999
CountryItaly
CityTrento
Period99/7/299/7/4

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Nagaya, T., & Toyama, Y. (1999). Decidability for left-linear growing term rewriting systems. In P. Narendran, & M. Rusinowitch (Eds.), Rewriting Techniques and Applications - 10th International Conference, RTA 1999, Proceedings (pp. 256-270). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1631). Springer Verlag. https://doi.org/10.1007/3-540-48685-2_22