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Abstract: . We survey recent results about ordering constraints on trees and discuss their applications. Our main interest lies in the family of recursive path orderings which enjoy the properties of being total, well-founded and compatible with the tree constructors. The paper includes some new results, in particular the undecidability of the theory of lexicographic path orderings in case of a non-unary signature. 1 Symbolic Constraints Constraints on trees are becoming popular in automated theorem... (Update)
Context of citations to this paper: More
.... under fixed signatures in [NRV99] NPhardness of the satisfiability problem is known, even for one single inequation, for all these cases [CT94]. All these decision procedures use at some point the fact that a constraint C can be effectively expressed as an equivalent...
...to a less general class of transfer functions. Our techniques also bear relation to earlier work on constraint solving in general [9 12, 28], especially that of solving set constraints [1 4,17,22 24,43] The class of tractable constraints we consider is closely related to de...
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1.0: Ordering Constraints on Trees - Comon, Treinen (1994) (Correct)
0.4: Constraints in Term Algebras (Short Survey) - Comon (Correct)
0.3: Unification of Infinite Sets of Terms Schematized by.. - Hermann, Galbavý (1996) (Correct)
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0.3: The First-Order Theory of Lexicographic Path Orderings is.. - Comon, Treinen (1997) (Correct)
0.3: Constraints in Computational Logics, International.. - Comon, Marché, .. (2001) (Correct)
0.3: More Problems in Rewriting - Dershowitz, Jouannaud, Klop (1993) (Correct)
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11: Solving symbolic ordering constraints - Comon - 1990
6: Satisfiability of systems of ordinal notation with the subterm property is decid.. (context) - Jouannaud, Okada - 1991
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BibTeX entry: (Update)
Hubert Comon and Ralf Treinen. Ordering constraints on trees. In Sophie Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1--14, Edinburgh, Scotland, 1994. Springer-Verlag. (Invited Lecture). http://citeseer.ist.psu.edu/article/comon94ordering.html More
@techreport{ comon94ordering,
author = "Hubert Comon and Ralf Treinen",
title = "Ordering Constraints on Trees",
number = "RR-94-12",
address = "Deutsches Forschungszentrum f{\"u}r K{\"u}nstliche Intelligenz GmbH\\Erwin-Schr{\"o}dinger Stra{ss}e\\Postfach 2080\\67608 Kaiserslautern\\Germany",
pages = "34",
year = "1994",
url = "citeseer.ist.psu.edu/article/comon94ordering.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
384 Simple word problems in universal algebras (context) - Knuth, Bendix - 1970
214 Orderings for term rewriting systems (context) - Dershowitz - 1982
125 Solving equations in abstract algebras: A rule-based survey .. (context) - Jouannaud, Kirchner - 1991
82 Two generalizations of the recursive path ordering (context) - Kamin, L'evy - 1980
74 Basic paramodulation and superposition (context) - Bachmair, Ganzinger et al. - 1992
64 Basic superposition is complete (context) - Nieuwenhuis, Rubio - 1992
58 Deduction with symbolic constraints (context) - Kirchner, Kirchner et al. - 1990
55 Theorem proving with ordering constrained clauses (context) - Nieuwenhuis, Rubio - 1992
52 On word problems in equational theories (context) - Hsiang, Rusinowitch - 1987
50 Semantic confluence tests and completion methods (context) - Plaisted - 1985
48 Disunification: a survey - Comon - 1991
47 Solving symbolic ordering constraints - Comon - 1990
41 A precedence-based total AC-compatible ordering (context) - Nieuwenhuis, Rubio - 1993
41 Encompassment properties and automata with constraints (context) - Caron, Coquid'e et al. - 1993
38 Simple LPO constraint solving methods - Nieuwenhuis - 1993
34 Any ground associative-commutative theory has a finite canon.. - Narendran, Rusinowitch - 1991
31 Decidability of the purely existential fragment of the theor.. (context) - Venkataraman - 1987
30 A new method for undecidability proofs of first order theori.. - Treinen - 1992
23 Satisfiability of systems of ordinal notations with the subt.. (context) - Jouannaud, Okada - 1991
20 Concatenation as a basis for arithmetic (context) - Quine - 1946
20 Equational formulas in order-sorted algebras (context) - Comon - 1990
15 The first-order theory of lexicographic path orderings is un.. - Comon, Treinen - 1993
9 About the theory of tree embedding - Boudet, Comon - 1993
6 Decidability of the existential theory of infinite terms wit.. (context) - Tulipani - 1994
4 Constraints in term algebras (context) - Comon - 1993
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