## Constraint ProgrammingBrian Mayoh, Enn Tyugu, Jaan Penjam Constraint programming is like an octopus spreading its tentacles into databases, operations research, artificial intelligence, and many other areas. The concept of constraint programming was introduced in artificial intelligence and graphics in the 1960s and 1970s. Now the related techniques are used and studied in many fields of computing. Different aspects of constraint processing are investigated in theoretical computer science, logic programming, knowledge representation, operations research, and related application domains. Constraint programming has been included in the lists of related topics of many conferences. Nevertheless, only in 1993 were the first forums held, devoted as a whole to this field of knowledge. These were the First Workshop on Principles and Practice of Constraint Programming (PPCP'93) which was held in Newport, Rhode Island, USA, April 28-30, the International Workshop on Constraint Processing (at CSAM'93) held in St. Petersburg, Russia, July 20-21, and the NATO Advanced Study Institute (NATO AS!) on Constraint Programming held in Parnu, Estonia, August 13-24. NATO A Sis are aimed to be schools bringing together leading researchers and practitioners from industry and academia in some area of knowledge to provide a concise picture of the work done and results obtained by different groups. This is intended for dissemination of advanced knowledge not yet taught regularly in of new topics university. However, ASis must also encourage the introduction into university curricula as well as foster international scientific contacts. |

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### Contents

1 | |

14 | |

B Mayoh 17 | 34 |

Constraint Solving Techniques | 51 |

Freuder 51 | 74 |

Foundations of Constraint Programming Approaches | 173 |

Constraint Programming Systems | 312 |

Appendix | 450 |

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### Common terms and phrases

abstract domain abstract interpretation agent algebraic algorithms application Artificial Intelligence atoms backtracking behaviour called cc program clause Computer Science concurrent constraint programming consider consistent constraint graph constraint hierarchy Constraint Logic Programming constraint network constraint programming constraint satisfaction problems constraint system construct constructor contextual corresponding defined Definition denote derivation element entailment equation event structure example finite fixpoint formula Freeman-Benson functional constraint Galois connection Gentzen given global goal graph production implementation infinite input interpretation interval arithmetic labels Lemma linear machine Montanari multiset nodes nondeterminism object-oriented object-oriented programming objects occurrence operation operational semantics partial order possible predicate Proc production programming languages read-only relation representing result rewrite rules Saraswat satisfied scheduling problem sequence solution solving specification statement straint subderivation subproblem techniques Theorem tion tokens tree Tyugu value propagation variables