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Abstract: this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction (Update)
Context of citations to this paper: More
...of a formula is the number of alternations of quanti ers in the prenex form. On the undecidability side of the border it was proved in [T90] and [T92] that the 3 part the theory is undecidable (this part contains the formulae whose quanti er pre x is of the form 9 8 9...
...even in the structure of finite feature trees. Our proof is based on an encoding of the Post Correspondence Problem using a technique of [33]. Once the undecidability of the first order theory of FT is settled, it remains to distinguish decidable fragments and their...
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16: Rewrite systems - Dershowitz, Jouannaud - 1990
14: Decidability of the purely existential fragment of the theory of term algebra (context) - Venkataraman - 1987
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BibTeX entry: (Update)
R. Treinen. A new method for undecidability proofs of first order theories. Journal of Symbolic Computation, 14(5):437--458, November 1992. http://citeseer.ist.psu.edu/article/treinen92new.html More
@inproceedings{ treinen90new,
author = "Ralf Treinen",
title = "A New Method for Undecidability Proofs of First Order Theories",
booktitle = "Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science",
volume = "472",
publisher = "Springer-Verlag",
editor = "K. V. Nori and C. E. Veni Madhavan",
pages = "48--62",
year = "1990",
url = "citeseer.ist.psu.edu/article/treinen92new.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990 ACM DBLP
370 Mathematical Introduction to Logic (context) - Enderton - 1972
229 Theory of Recursive Functions and Effective Computability (context) - Jr - 1987 ACM
214 Orderings for term-rewriting systems (context) - Dershowitz - 1982 DBLP
161 Fundamentals of Algebraic Specification (context) - Ehrig, Mahr - 1985
134 Unification theory - Siekmann - 1989 ACM DBLP
129 Termination of rewriting (context) - Dershowitz - 1987 ACM DBLP
114 Fundamental properties of infinite trees (context) - Courcelle - 1983 DBLP
114 Building-in equational theories (context) - Plotkin - 1972
105 The problem of solvability of equations in a free semi-group (context) - Makanin - 1977
72 Logic for Computer Science (context) - Gallier - 1986 ACM
70 Equational problems and disunification (context) - Comon, Lescanne - 1989 ACM DBLP
67 A variant of a recursively unsolvable problem (context) - Post - 1946
62 A unification algorithm for associative-commutative function.. (context) - Stickel - 1981
48 Disunification: A survey - Comon - 1991 DBLP
47 Solving symbolic ordering constraints - Comon - 1990 DBLP
31 Decidability of the purely existential fragment of the theor.. (context) - Venkataraman - 1987
23 Satisfiability of systems of ordinal notation with the subte.. (context) - Jouannaud, Okada - 1991
23 Associative-commutative unification (context) - Fages - 1987 ACM DBLP
20 Concatenation as a basis for arithmetic (context) - Quine - 1946 DBLP
17 Undecidable Theories (context) - Tarski, Mostowski et al. - 1953
16 A simple method for undecidability proofs and some applicati.. (context) - Rabin - 1965
15 M'ethodes et Outils de Conception Syst'ematique d'Algorithme.. (context) - Kirchner - 1985
9 Unsolvable problems (context) - Davis - 1977
8 Formal languages and power series (context) - Salomaa - 1990 ACM DBLP
6 Unification et Disunification (context) - Comon - 1988
5 Complete axiomatisations of the algebra of finite (context) - Maher - 1988
3 Enumerable sets are diophantine (context) - Matijacevic - 1970
1 Decidability of the existential theory of infinite terms wit.. (context) - Tulipani - 1993 ACM DBLP
1 Undecidability and essential undecidability in arithmetic (context) - Tarski, Mostowski et al. - 1953
1 Unification of bags and sets (context) - Livesey, Siekmann - 1976
1 Kurt Godel (context) - Feferman - 1986
1 the solvability of equational problems (context) - Burckert, Schmidt-Schauss - 1989
1 On equational theories (context) - Burckert, Herold et al. - 1989
1 A general method in proofs of undecidability (context) - Tarski - 1953
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.lri.fr/~treinen/publications.html): More
Records for Logic Programming - Smolka, Treinen (1994) (Correct)
Constraint Deduction in an Interval-based Temporal Logic - Jana Koehler, Ralf Treinen (1993) (Correct)
Feature Constraints with First-Class Features - Treinen (1993) (Correct)
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