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A New Method for Undecidability Proofs of First Order Theories (1992)  (Make Corrections)  (30 citations)
Ralf Treinen
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science



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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 (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...

Cited by:   More
The First-Order Theory of Subtyping Constraints - Su, Aiken, Niehren, Priesnitz   (Correct)
On Equality Up-to Constraints over Finite Trees, Context .. - Niehren, Pinkal..   (Correct)
The First-Order Theory of Ordering Constraints over Feature .. - Müller, Niehren, Treinen   (Correct)

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1.3:   A New Method for Undecidability Proofs of First Order Theories - Treinen (1992)   (Correct)
0.3:   The First-Order Theory of Lexicographic Path Orderings is.. - Comon, Treinen (1997)   (Correct)
0.2:   Ordering Constraints on Trees - Comon, Treinen (1994)   (Correct)

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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
11:   Complete axiomatizations of some quotient term algebras - Comon - 1993

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/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/treinen92new.html" }
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Documents on the same site (http://www.ps.uni-sb.de/Papers/abstracts/):   More
Set-Based Failure Analysis for Logic Programs and.. - Podelski, Charatonik, .. (1999)   (Correct)
Type Inference for First-Class Messages with Feature Constraints - Müller, Nishimura   (Correct)
Entailment of Non-Structural Subtype Constraints - Niehren, Priesnitz (1999)   (Correct)

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