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Abstract: We extend the Knuth-Bendix completion procedure from equational rewriting to rewriting with non-symmetric transitive relations and quasi-orderings. The main di erences are the following: Speci cation of the general non-ground case seems beyond rst-order logic. It is within rst-order logic when terms are linear or functions non-monotonic. The procedure requires critical-pair computations and need not terminate even in the ground case. Simpli cation is not don't care non-deterministic,... (Update)
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BibTeX entry: (Update)
G. Struth. Knuth-Bendix completion for non-symmetric transitive relations. In M. van den Brand and R. Verma, editors, Second International Workshop on RuleBased Programming (RULE2001), volume 59 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers, 2001. http://citeseer.ist.psu.edu/struth01knuthbendix.html More
@inproceedings{ struth01knuthbendix,
author = "Georg Struth",
title = "Knuth-Bendix Completion for Non-Symmetric Transitive Relations",
booktitle = "Second International Workshop on Rule-Based Programming (RULE2001)",
volume = "59(4)",
publisher = "Elsevier Science Publishers",
address = "Amsterdam",
editor = "Mark van den Brand and Rakesh Verma",
year = "2001",
url = "citeseer.ist.psu.edu/struth01knuthbendix.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
353 Term rewriting and all that (context) - Baader, Nipkow - 1998
75 Completion of rewrite systems with membership constraints - Comon - 1992
58 Canonical Equational Proofs (context) - Bachmair - 1991
43 Termination orderings for associative-commutative rewriting .. (context) - Bachmair, Plaisted - 1985
42 Rewrite techniques for transitive relations - Bachmair, Ganzinger - 1994
33 Extension of the associative path ordering to a chain of ass.. (context) - Delor, Puel - 1993
21 Bi-rewrite systems - Levy, Agust - 1996
12 Canonical Transformations in Algebra (context) - Struth - 1998
7 Normalization via rewrite closures - Bachmair, Ramakrishnan et al. - 1999
5 Buchberger's algorithm: The term rewriter's point of view (context) - undgen - 1996
3 A decision algorithm for stratied context unication (context) - Schmidt-Schauss - 1999
3 Non-symmetric rewriting - Struth - 1996
3 Rewriting as a unied model of concurrency (context) - Meseguer - 1990
3 An algebra of resolution (context) - Struth
[Article contains additional citations not shown here]
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