Ordering Constraints on Trees

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]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[2]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[3]  Albert Rubio,et al.  A Precedence-Based Total AC-Compatible Ordering , 1993, RTA.

[4]  David A. Plaisted,et al.  Semantic Confluence Tests and Completion Methods , 1985, Inf. Control..

[5]  C. Kirchner,et al.  Deduction with symbolic constraints , 1990 .

[6]  Hubert Comon.  Equational Formulas in Order-Sorted Algebras , 1990 .

[7]  M. R. Spiegel.  E and M , 1981 .

[8]  Michaël Rusinowitch,et al.  Any Gound Associative-Commutative Theory Has a Finite Canonical System , 1991, RTA.

[9]  H. Comon.  SOLVING SYMBOLIC ORDERING CONSTRAINTS , 1990 .

[10]  Jean-Pierre Jouannaud,et al.  Satisfiability of Systems of Ordinal Notations with the Subterm Property is Decidable , 1991, ICALP.

[11]  W. V. Quine,et al.  Concatenation as a basis for arithmetic , 1946, Journal of Symbolic Logic.

[12]  Max Dauchet,et al.  Encompassment Properties and Automata with Constraints , 1993, RTA.

[13]  Michaël Rusinowitch,et al.  On Word Problems in Equational Theories , 1987, ICALP.

[14]  K. N. Venkataraman,et al.  Decidability of the purely existential fragment of the theory of term algebras , 1987, JACM.

[15]  Hubert Comon,et al.  Disunification: A Survey. , 1991 .

[16]  Hubert Comon-Lundh,et al.  About the Theory of Tree Embedding , 1993, TAPSOFT.

[17]  Albert Rubio,et al.  Theorem Proving with Ordering Constrained Clauses , 1992, CADE.

[18]  Ralf Treinen.  A New Method for Undecidablity Proofs of First Order Theories , 1992, J. Symb. Comput..

[19]  Donald E. Knuth,et al.  Simple Word Problems in Universal Algebras††The work reported in this paper was supported in part by the U.S. Office of Naval Research. , 1970 .

[20]  Hubert Comon.  Constraints in Term Algebras (Short Survey) , 1993 .

[21]  Albert Rubio,et al.  Basic Superposition is Complete , 1992, ESOP.

[22]  Robert Nieuwenhuis,et al.  Simple LPO Constraint Solving Methods , 1993, Inf. Process. Lett..

[23]  Sauro Tulipani.  Decidability of the Existential Theory of Infinite Terms with Subterm Relation , 1994, Inf. Comput..

[24]  Nachum Dershowitz.  Orderings for Term-Rewriting Systems , 1979, FOCS.

[25]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[26]  Claude Kirchner,et al.  Solving Equations in Abstract Algebras: A Rule-Based Survey of Unification , 1991, Computational Logic - Essays in Honor of Alan Robinson.

[27]  Wayne Snyder,et al.  Basic Paramodulation and Superposition , 1992, CADE.