License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.RTA.2010.341
URN: urn:nbn:de:0030-drops-26625
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2662/
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Durand, Irène ; Sénizergues, Géraud ; Sylvestre, Marc

Termination of linear bounded term rewriting systems

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Abstract

For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting.
We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse k-bounded problems are decidable.
The k-bounded class (BO(k)) is, by definition, the set of linear systems for
which every derivation can be replaced by a k-bounded derivation. In general, for BO(k) systems, the uniform (respectively inverse uniform) k-bounded termination problem is not equivalent to the uniform (resp. inverse uniform) termination problem, and the k-bounded (respectively inverse k-bounded) termination problem is not equivalent to the termination (respectively inverse termination) problem.
This leads us to
define more restricted classes for which these problems are equivalent: the classes BOLP(k) of
k-bounded systems that have the length preservation property. By definition, a system is BOLP(k) if every derivation of length n can be replaced by a k-bounded derivation of length n.
We define the class BOLP of bounded systems that have the length preservation property as the union of all the BOLP(k) classes.
The class BOLP contains (strictly) several already known classes of systems:
the inverse left-basic semi-Thue systems,
the linear growing term rewriting systems, the inverse Linear-Finite-Path-Ordering systems, the strongly bottom-up systems.

BibTeX - Entry

@InProceedings{durand_et_al:LIPIcs:2010:2662,
  author =	{Ir{\`e}ne Durand and G{\'e}raud S{\'e}nizergues and Marc Sylvestre},
  title =	{{Termination of linear bounded term rewriting systems}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{341--356},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Christopher Lynch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2662},
  URN =		{urn:nbn:de:0030-drops-26625},
  doi =		{10.4230/LIPIcs.RTA.2010.341},
  annote =	{Keywords: Term rewriting, termination, rewriting strategy}
}

Keywords: Term rewriting, termination, rewriting strategy
Collection: Proceedings of the 21st International Conference on Rewriting Techniques and Applications
Issue Date: 2010
Date of publication: 06.07.2010

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