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Abstract: this paper we further improve and sharpen the above weak undecidability results by showing that no decision algorithm can decide the of any given finite, simultaneously (1) finitely terminating, (2) linear, and (3) confluent rewrite system. All the preceding proofs constructed nonconfluent systems. For comparison, [11] proved an analogous result for non-confluent terminating systems and and [6] for divergent non-confluent systems (Update)
Context of citations to this paper: More
.... of linear Noetherian rewrite systems in [20] and to the 9 8 9 fragment for the class of linear Noetherian rewrite systems in [32, 33]. In this paper we restrict the class of rewrite systems for which the theory of onestep rewriting is undecidable to the class of linear, ultra...
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BibTeX entry: (Update)
Vorobyov, S. The undecidability of the first order theories of one-step rew riting in linear canonical systems. Tech. Rep. MPI-I-98-2-009, Max Planck Institute, 1998. http://citeseer.ist.psu.edu/vorobyov02undecidability.html More
@misc{ vorobyov98undecidability,
author = "S. Vorobyov",
title = "The undecidability of the first order theories of one-step rew riting in
linear canonical systems",
text = "Vorobyov, S. The undecidability of the first order theories of one-step
rew riting in linear canonical systems. Tech. Rep. MPI-I-98-2-009, Max Planck
Institute, 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/vorobyov02undecidability.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
384 Simple word problems in universal algebras (context) - Knuth, Bendix - 1970
177 Computation: Finite and Infinite Machines (context) - Minsky - 1967
50 Semantic confluence tests and completion methods (context) - Plaisted - 1985
43 Recursive unsolvability of Post's problem of `tag' and other.. (context) - Minsky - 1961
42 The theory of ground rewrite systems is decidable (context) - Dauchet, Tison - 1990
41 Encompassment properties and automata with constraints (context) - Caron, Coquide et al. - 1993
27 More problems in rewriting - Dershowitz, Jouannaud et al. - 1993
27 Unsolvable Classes of Quantificational Formulas (context) - Lewis - 1979
20 Concatenation as a basis for arithmetic (context) - Quine - 1946
12 The first-order theory of one step rewriting is undecidable (context) - Treinen - 1996
11 Problems in rewriting III - Dershowitz, Jouannaud et al. - 1995
9 Undecidability of the first-order theory of one step right g.. (context) - Marcinkowski - 1997
7 Automata for reduction properties solving (context) - Dauchet, Caron et al. - 1995
5 On Trees and Rewriting (context) - Vorobyov - 1995
5 Grid structure and undecidable constraint theories - Seynhaeve, Tommasi et al. - 1997
3 the decidability of ground reducibility (context) - Kaplan, Choquer - 1986
1 Equations and rewrite rules: A surve (context) - Huet, Oppen - 1980
1 A decreasing conditional rewrite system with # 1 -complete g.. (context) - Vorobyov - 1998
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