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Abstract: We present a new criterion for confluence of (possibly) non-terminating leftlinear term rewriting systems. The criterion is based on certain strong joinability properties of parallel critical pairs . We show how this criterion relates to other well-known results, consider some special cases and discuss some possible extensions. 1 Introduction and Overview Computation formalisms which are based on rewriting systems heavily rely on the fundamental properties of termination and confluence. For... (Update)
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.... diamond property of a parallel reduction, which is inspired by Gramlich s characterization of the strong confluence of a parallel reduction [Gra96]. Lemma 13 (parallel moves) We have k Delta ffl Gamma k Delta k ( k Delta k k Delta k . Proof. The implication...
.... property of the parallel reduction, which is inspired by Gramlich s characterisation of strong confluence of the parallel reduction [Gra96]. Lemma 2.4 (parallel moves) We have k 1 k 1 k ( k 1 k k 1 k . Proof. The implication from right to left is obvious by...
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BibTeX entry: (Update)
B. Gramlich. Confluence without termination via parallel critical pairs. In Proceedings of the 21st International Colloquium on Trees in Algebra and Programming (CAAP'96), 1996. Lecture Notes in Computer Science 1059, pp. 211-225. http://citeseer.ist.psu.edu/article/gramlich96confluence.html More
@inproceedings{ gramlich96confluence,
author = "Bernhard Gramlich",
title = "Confluence without Termination via Parallel Critical Pairs",
booktitle = "Colloquium on Trees in Algebra and Programming",
pages = "211-225",
year = "1996",
url = "citeseer.ist.psu.edu/article/gramlich96confluence.html" }
Citations (may not include all citations):474 Term rewriting systems - Klop - 1992
247 Confluent reductions: Abstract properties and applications t.. (context) - Huet - 1980
134 Unification theory - Baader, Siekmann - 1994
54 Tree-manipulating systems and Church-Rosser theorems (context) - Rosen - 1973
34 Higher-order rewrite systems and their confluence - Mayr, Nipkow - 1994
29 Term rewriting and equational reasoning (context) - Avenhaus, Madlener - 1990
28 On theories with a combinatorial definition of equivalence (context) - Newman - 1942
23 Open problems in rewriting - Dershowitz, Jouannaud et al. - 1991
22 Only prime superpositions need be considered in the Knuth-Be.. (context) - Kapur, Musser et al. - 1988
17 Critical pair criteria for completion (context) - Bachmair, Dershowitz - 1988
14 Commutativity of term rewriting systems (context) - Toyama - 1988
10 mail communication (context) - Toyama - 1995
10 Confluence by decreasing diagrams (context) - Oostrom - 1994
3 the Church-Rosser property of Eoverlapping and simple-right-.. (context) - Oyamaguchi, Toyama - 1994
2 Basic Research Laboratories (context) - Oostrom, Technical - 1994
1 A confluence criterion based on the generalized Newman lemma (context) - Kuchlin - 1985
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