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Abstract: For a hierarchy of properties of term rewriting systems related to confluence we prove relative undecidability, i.e., for implications X Y in the hierarchy the property X is undecidable for term rewriting systems satisfying Y . For some of the implications either X or is semi-decidable, for others neither X nor is semi-decidable. We prove most of these results for linear term rewrite systems. (Update)
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BibTeX entry: (Update)
@misc{ geser-relative,
author = "Alfons Geser and Aart Middeldorp",
title = "Relative Undecidability in Term Rewriting Part 2: The Confluence Hierarchy",
url = "citeseer.ist.psu.edu/599497.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
474 Term rewriting systems - Klop - 1992
353 Term Rewriting and All That (context) - Baader, Nipkow - 1998
247 Confluent reductions: Abstract properties and applications t.. (context) - Huet - 1980
89 Termination of term rewriting: Interpretation and type elimi.. - Zantema - 1994
67 A variant of a recursively unsolvable problem (context) - Post - 1946
45 Decision problems for semi-Thue systems with a few rules - Matiyasevich, Senizergues - 1996
19 On ground-confluence of term rewriting systems (context) - Kapur, Narendran et al. - 1980
17 Equations and rewrite rules: A survey (context) - Huet, Oppen - 1980
12 Modularity of confluence: A simplified proof - Klop, Middeldorp et al. - 1994
9 Unification in a combination of arbitrary disjoint equationa.. (context) - Schmidt-Schau - 1989
8 the uniform halting problem for term rewriting systems (context) - Huet, Lankford - 1978
6 Algorithms and reductions for rewriting problems - Verma, Rusinowitch et al. - 1998
5 Relative undecidability in term rewriting - Geser, Middeldorp et al. - 1997
5 Relative undecidability in term rewriting - Geser, Middeldorp et al.
4 Journal of Universal Computer Science (context) - Aoto, Toyama et al. - 1997
1 The property FDT is undecidable for finitely presented monoi.. (context) - Otto, Sattler-Klein - 2000
1 Modular termination of rconsistent and left-linear term rewr.. (context) - Schmidt-Schau, Marchiori et al. - 1995
1 New undecidability results for finitely presented monoids (context) - Sattler-Klein - 1997
1 Modularity in many-sorted term rewriting systems (context) - Pol - 1992
Documents on the same site (http://www.score.is.tsukuba.ac.jp/~ami/research/papers/jp.html): More
Simple Termination of Rewrite Systems - Middeldorp, Zantema (1997) (Correct)
Modularity of Confluence: A Simplified Proof - Klop, Middeldorp, Toyama, de.. (1994) (Correct)
Strongly Sequential and Inductively Sequential Term.. - Hanus, Lucas, Middeldorp (1998) (Correct)
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