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Towards a Declarative Query and Transformation Language for XML and Semistructured Data: Simulation Unification
, 2002
"... The growing importance of XML as a data interchange standard demands languages for data querying and transformation. Since the mid 90es, several such languages have been proposed that are inspired from functional languages (such as XSLT [1]) and/or database query languages (such as XQuery [2]). ..."
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Cited by 79 (38 self)
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The growing importance of XML as a data interchange standard demands languages for data querying and transformation. Since the mid 90es, several such languages have been proposed that are inspired from functional languages (such as XSLT [1]) and/or database query languages (such as XQuery [2]). This paper addresses applying logic programming concepts and techniques to designing a declarative, rulebased query and transformation language for XML and semistructured data.
A New Method for Undecidability Proofs of First Order Theories
 Journal of Symbolic Computation
, 1992
"... 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 ..."
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Cited by 30 (7 self)
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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
Adventures in AssociativeCommutative Unification
 Journal of Symbolic Computation
, 1989
"... We have discovered an efficient algorithm for matching and unification in associativecommutative (AC) equational theories. In most cases of AC unification our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associativecommutative unificat ..."
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Cited by 22 (0 self)
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We have discovered an efficient algorithm for matching and unification in associativecommutative (AC) equational theories. In most cases of AC unification our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associativecommutative unification techniques. The algorithm efficiently utilizes powerful constraints to eliminate much of the search involved in generating valid substitutions. Moreover, it is able to generate solutions lazily, enabling its use in an SLDresolutionbased environment like Prolog. We have found the method to run much faster and use less space than other associativecommutative unification procedures on many commonly encountered AC problems. 1 Introduction Associativecommutative (AC) equational theories surface in a number of computer science applications, including term rewriting, automatic theorem proving, software verification, and database retrieval. As a simple example, consider trying to find a sub...
On the Unification Problem for Cartesian Closed Categories (Extended Abstract)
 IN PROCEEDINGS, EIGHTH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1989
"... Cartesian closed categories (CCC's) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce and Longo leads to se ..."
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Cited by 19 (5 self)
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Cartesian closed categories (CCC's) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NPcomplete. Furthermore, the problem of matching in CCC's is NPcomplete when the subject term is irreduc...
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
DoubleExponential Complexity of Computing a Complete Set of ACUnifiers
 In Proceedings 7th IEEE Symposium on Logic in Computer Science
"... A new algorithm for computing a complete set of unifiers for two terms involving associativecommutative function symbols is presented. The algorithm is based on a nondeterministic algorithm given by the authors in 1986 to show the NPcompleteness of associativecommutative unifiability. The algori ..."
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Cited by 17 (0 self)
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A new algorithm for computing a complete set of unifiers for two terms involving associativecommutative function symbols is presented. The algorithm is based on a nondeterministic algorithm given by the authors in 1986 to show the NPcompleteness of associativecommutative unifiability. The algorithm is easy to understand, its termination can be easily established. More importantly, its complexity can be easily analyzed and is shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a doubleexponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associativecommutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense. This is the first associativecommutative unification algorithm whose complexity has been completely analyzed. The approach can also be used to show a singl...
Paramodulation with Builtin ACTheories and Symbolic Constraints
 Journal of Symbolic Computation
, 1996
"... this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying the ..."
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Cited by 11 (6 self)
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this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying the constraint T . In a constrained equation
Solving Linear Diophantine Constraints Incrementally
 PROC. OF 10TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1993
"... In this paper, we show how to handle linear Diophantine constraints incrementally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems [4, 5]. The basic algorithm is based on a certain enumeration of the potential solution ..."
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Cited by 11 (0 self)
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In this paper, we show how to handle linear Diophantine constraints incrementally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems [4, 5]. The basic algorithm is based on a certain enumeration of the potential solutions of a system, and termination is ensured by an adequate restriction on the search. This algorithm generalizes a previous algorithm due to Fortenbacher [2], which was restricted to the case of a single equation. Note that using Fortenbacher's algorithm for solving systems of Diophantine equations by repeatedly applying it to the successive equations is completely unrealistic: the tuple of variables in the solved equation must then be substituted in the rest of the system by a linear combination of the minimal solutions found in which the coefficients stand for new variables. Unfortunately, the number of these minimal solutions is actually exponential in both the number of variables and the v...