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International Conference on Rewriting Techniques and Applications

RTA 2002: Rewriting Techniques and Applications pp 267–280Cite as

Loops of Superexponential Lengths in One-Rule String Rewriting

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

Abstract

Loops are the most frequent cause of non-termination in string rewriting. In the general case, non-terminating, non-looping string rewriting systems exist, and the uniform termination problem is undecidable. For rewriting with only one string rewriting rule, it is unknown whether non-terminating, non-looping systems exist and whether uniform termination is decidable. If in the one-rule case, non-termination is equivalent to the existence of loops, as McNaughton conjectures, then a decision procedure for the existence of loops also solves the uniform termination problem. As the existence of loops of bounded lengths is decidable, the question is raised how long shortest loops may be. We show that string rewriting rules exist whose shortest loops have superexponential lengths in the size of the rule.

This work was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-97046 while the author was in residence at ICASE.

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Author information

Authors and Affiliations

  1. ICASE, NASA Langley Research Center, Mail Stop 132C, Hampton, VA, 23681

    Alfons Geser

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  1. Alfons Geser
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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Geser, A. (2002). Loops of Superexponential Lengths in One-Rule String Rewriting. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_19

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  • DOI: https://doi.org/10.1007/3-540-45610-4_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

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