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Principles of Constraint Programming
, 2000
"... Introduction 1.1 Preliminaries Constraint programming is an alternative approach to programming in which the programming process is limited to a generation of requirements (constraints) and a solution of these requirements by means of general or domain specific methods. The general methods are us ..."
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Cited by 260 (3 self)
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Introduction 1.1 Preliminaries Constraint programming is an alternative approach to programming in which the programming process is limited to a generation of requirements (constraints) and a solution of these requirements by means of general or domain specific methods. The general methods are usually concerned with techniques of reducing the search space and with specific search methods. In contrast, the domain specific methods are usually provided in the form of special purpose algorithms or specialised packages, usually called constraint solvers. Typical examples of constraint solvers are: ffl a program that solves systems of linear equations, ffl a package for linear programming, ffl an implementation of the unification algorithm, a cornerstone of automated theorem proving. Problems that can be solved in a natural way by means of constraint programming are usually those for which efficient algorithms are
The Essence of Constraint Propagation
 CWI QUARTERLY VOLUME 11 (2&3) 1998, PP. 215 { 248
, 1998
"... We show that several constraint propagation algorithms (also called (local) consistency, consistency enforcing, Waltz, ltering or narrowing algorithms) are instances of algorithms that deal with chaotic iteration. To this end we propose a simple abstract framework that allows us to classify and comp ..."
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Cited by 106 (6 self)
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We show that several constraint propagation algorithms (also called (local) consistency, consistency enforcing, Waltz, ltering or narrowing algorithms) are instances of algorithms that deal with chaotic iteration. To this end we propose a simple abstract framework that allows us to classify and compare these algorithms and to establish in a uniform way their basic properties.
From Chaotic Iteration to Constraint Propagation
 In Proc. of the 24th International Colloquium on Automata, Languages and Programming (ICALP'97) (invited lecture), LNCS 1256
, 1997
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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Cited by 25 (2 self)
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Constraint programming viewed as rulebased programming
 PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We study here a natural situation when constraint programming can be entirely reduced to rulebased programming. To this end we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these constraints and limit t ..."
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Cited by 21 (2 self)
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We study here a natural situation when constraint programming can be entirely reduced to rulebased programming. To this end we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider here two types of rules. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyperarc consistency in (Marriott & Stuckey, 1998)). For Boolean constraints rule consistency coincides with the closure under the wellknown propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rulebased characterization of arc consistency. To show feasibility of this rulebased approach to constraint programming we show how both types of rules can be automatically generated, as CHR rules of (Frühwirth, 1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz’s language for describing polyhedral scenes, and Allen’s qualitative approach to temporal logic. Note. A preliminary version of this article appeared as (Apt & Monfroy, 1999).
Constraint Contextual Rewriting
, 1998
"... We are interested in the problem of integrating decision procedures with rewriting as in many stateoftheart verication systems. We dene Constraint Contextual Rewriting (CCR) as a generalization of contextual rewriting, whereby the rewriting context is processed by the available decision proced ..."
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Cited by 20 (7 self)
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We are interested in the problem of integrating decision procedures with rewriting as in many stateoftheart verication systems. We dene Constraint Contextual Rewriting (CCR) as a generalization of contextual rewriting, whereby the rewriting context is processed by the available decision procedures. We show how CCR accounts for some of the most important integration schemas adopted in stateoftheart veri cation systems. The rulebased presentation of CCR given in this paper contrasts the practice of describing the integration either by examples or in informal ways with highlevel ideas intermixed with implementation details. Important properties (e.g. soundness) of the proposed integration schema can be formally stated and proved. Moreover, the approach is amenable of operationalization. This has allowed us to easily fastprototype and validate the integration schemas described in this paper.
Automatic Generation of CHR Constraint Solvers
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2005
"... In this paper, we present a framework for automatic generation of CHR solvers given the logical speci cation of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to check the validity of the rules. Compared to previous work ( ..."
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Cited by 15 (4 self)
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In this paper, we present a framework for automatic generation of CHR solvers given the logical speci cation of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to check the validity of the rules. Compared to previous work (Apt & Monfroy, 1999; Ringeissen & Monfroy, 2000; Abdennadher & Rigotti, 2000; Abdennadher & Rigotti, 2001a), where dierent methods for automatic generation of constraint solvers have been proposed, our approach enables the generation of more expressive rules (even recursive and splitting rules) that can be used directly as CHR solvers.
Automatic Generation of RuleBased Constraint Solvers over Finite Domains
, 2002
"... A general approach to implement propagation and... In this paper, we propose a method for generating propagation and simplification rules for constraints over finite domains defined extensionally by e.g. a truth table or their tuples. The generation of rules is performed in two steps. First, propaga ..."
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Cited by 14 (2 self)
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A general approach to implement propagation and... In this paper, we propose a method for generating propagation and simplification rules for constraints over finite domains defined extensionally by e.g. a truth table or their tuples. The generation of rules is performed in two steps. First, propagation rules are generated. Propagation rules do not rewrite constraints but add new ones. Thus, the constraint store may contain superuous constraints. Removing these constraints not only allows saving of space but also decreases the cost of constraint solving. Constraints can be removed using simplification rules. Thus, in a second step some propagation rules are transformed into simplification rules. Furthermore, we show that...
Temporal Reasoning and Constraint Programming  A Survey
 CWI Quarterly
, 1998
"... Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . ..."
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Cited by 8 (1 self)
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Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . . . . . . . 9 1.3 Temporal reasoning and Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Temporal Reasoning with metric information . . . . . . . 14 1.3.2 Qualitative approach based on Allen's interval algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Mixed approaches . . . . . . . . . . . . . . . . . . . . . . 15 2 Temporal Reasoning and Constraint Programming 16 2.1 Temporal Constraints with metric information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 A first order language . . . . . . . . . . . . . . . . . . . . 16 2.1.2 The original Temporal Constraint Problem . .
A Language for Experimenting with Declarative Paradigms
"... Constraint Handling Rules is a rulebased language for writing constraint solvers either from scratch or by modifying existing solvers. Currently, CHR ..."
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Cited by 7 (0 self)
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Constraint Handling Rules is a rulebased language for writing constraint solvers either from scratch or by modifying existing solvers. Currently, CHR