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Abstract: By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the 9888-theory of one step rewriting of an arbitrary nite linear conuent nitely terminating term rewriting system (weak undecidability). We also present a xed such system with undecidable -theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind. (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/article/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/article/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
43 Recursive unsolvability of Post's problem of `tag' and other.. (context) - Minsky - 1961
41 Encompassment properties and automata with constraints (context) - Caron, Coquid et al. - 1993
27 More problems in rewriting - Dershowitz, Jouannaud et al. - 1993
20 Concatenation as a basis for arithmetic (context) - Quine - 1946
17 Equations and rewrite rules: a survey (context) - Huet, Oppen - 1980
11 Computation: Finite and In nite Machines (context) - Minsky - 1967
11 Problems in rewriting III - Dershowitz, Jouannaud et al. - 1995
9 The rst-order theory of one step rewriting is undecidable (context) - Treinen - 1996
7 Automata for reduction properties solving (context) - Dauchet, Caron et al. - 1995
5 Grid structure and undecidable constraint theories - Seynhaeve, Tommasi et al. - 1997
4 Undecidability of the rst-order theory of one step right gro.. (context) - Marcinkowski - 1997
3 The rst-order theory of one step rewriting in linear noether.. (context) - Vorobyov - 1997
3 Unsolvable Classes of Quanti cational Formulas (context) - Lewis - 1979
3 Semantic con uence tests and completion methods (context) - Plaisted - 1985
3 the decidability of ground reducibility (context) - Kaplan, Choquer - 1986
2 The elementary theory of one-step rewriting is undecidable - Vorobyov - 1995
1 A decreasing conditional rewrite system with 1 -complete g.. (context) - Vorobyov - 1998
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