The Role of Commutativity in Constraint Propagation Algorithms

Constraint propagation algorithms form an important part of most of the constraint programming systems. We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In this framework we proceed in two steps. First, we introduce a generic iteration algorithm on partial orderings and prove its correctness in an abstract setting. Then we instantiate this algorithm with specific partial orderings and functions to obtain specific constraint propagation algorithms. In particular, using the notions commutativity and semi-commutativity, we show that the {\tt AC-3}, {\tt PC-2}, {\tt DAC} and {\tt DPC} algorithms for achieving (directional) arc consistency and (directional) path consistency are instances of a single generic algorithm. The work reported here extends and simplifies that of Apt \citeyear{Apt99b}.Comment: 35 pages. To appear in ACM TOPLA

Finite domain constraint programming systems

Tutorial at CP'2002, Principles and Practice of Constraint Programming. Powerpoint slides.</p

General Properties and Termination Conditions for Soft Constraint Propagation

Soft constraints based on semirings are a generalization of classical constraints, where tuples of variables\u27 values in each soft constraint are associated to elements from an algebraic structure called semiring. This framework is able to express, for example, fuzzy, classical, weighted, valued and over-constrained constraint problems. Classical constraint propagation has been extended and adapted to soft constraints by defining a schema for soft constraint propagation [8]. On the other hand, in [1-3] it has been proven that most of the well known constraint propagation algorithms for classical constraints can be cast within a single schema. In this paper we combine these two schemas and we provide a more general framework where the schema of [3] can be used for soft constraints. In doing so, we generalize the concept of soft constraint propagation, and we provide new sufficient and independent conditions for its termination

Constraint propagation in Mozart

This thesis presents constraint propagation in Mozart which is based on computational agents called propagators. The thesis designs, implements, and evaluates propagator-based propagation engines. A propagation engine is split up in generic propagation services and domain specific domain solvers which are connected by a constraint programming interface. Propagators use filters to perform constraint propagation. The interface isolates filters from propagators such that they can be shared among various systems. This thesis presents the design and implementation of a finite integer set domainsolver for Mozart which reasons over bound and cardinality approximations of sets.The solver cooperates with a finite domain solver to improve its propagation and expressiveness. This thesis promotes constraints to first-class citizens and thus, provides extra control over constraints. Novel programming techniques taking advantage of the first-class status of constraints are developed and illustrated.Diese Dissertation beschreibt Constraint-Propagierung in Mozart, die auf Berechnungsagenten, Propagierer genannt, basiert. Die Dissertation entwirft, implementiert und evaluiert Propagierer-basierte Propagierungsmaschinen. Eine Propagierungsmaschine ist aufgeteilt in generische Propagierungsdienste und domänenspezifische Domänenlöser, die durch eine Schnittstelle zur Constraint-Programmierung miteinander verbunden sind. Propagierer benutzen Filter, um Constraints zu propagieren. Die Schnittstelle isoliert Filter von Propagierern, so dass Programmkodes von Filtern von verschiedenen Systemen genutzt werden können. Diese Dissertation präsentiert den Entwurf und die Implementierung eines Domänenlösers über endliche Mengen von ganzen Zahlen für Mozart, die über Mengen- und Kardinalitätsschranken approximiert werden. Dieser kooperiert mit einem Löser über endlichen Bereichen, um die Propagierung und die Ausdrucksfähigkeit zu verbessern. Diese Dissertation erhebt Constraints zu emanzipierten Datenstrukturen und stellt auf dieseWeise zusätzliche Steuerungsmöglichkeiten über Constraints zur Verfügung. Des Weiteren werden neuartige Programmiertechniken für emanzipierte Constraints entwickelt und demonstriert