Constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. In Constraint Processing, Rina Dechter synthesizes these contributions, as well as her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms.

This volume contains selected and thoroughly revised papers plus contributions from invited speakers presented at the First International Workshop on C- straint Solving and Language Processing, held in Roskilde, Denmark, September 1–3, 2004. Constraint Programming and Constraint Solving, in particular Constraint Logic Programming, appear to be a very promising platform, perhaps the most promising present platform, for bringing forward the state of the art in natural language processing, this due to the naturalness in speci?cation and the direct relation to e?cient implementation. Language, in the present context, may - fer to written and spoken language, formal and semiformal language, and even general input data to multimodal and pervasive systems, which can be handled in very much the same ways using constraint programming. The notion of constraints, with slightly di?ering meanings, apply in the ch- acterization of linguistic and cognitive phenomena, in formalized linguistic m- els as well as in implementation-oriented frameworks. Programming techniques for constraint solving have been, and still are, in a period with rapid devel- ment of new e?cient methods and paradigms from which language processing can pro?t. A common metaphor for human language processing is one big c- straintsolvingprocessinwhichthedi?erent(-lyspeci?ed)linguisticandcognitive phases take place in parallel and with mutual cooperation, which ?ts quite well with current constraint programming paradigms.

The Constraint Solving and Language Processing (CSLP) workshop considers the role of constraints in the representation of language and the implementation of language processing applications. This theme should be interpreted inclusively: it includes contributions from linguistics, computer science, psycholinguistics and related areas, with a particular interest in interdisciplinary perspectives. Constraints are widely used in linguistics, computer science, and psychology. How they are used, however, varies widely according to the research domain: knowledge representation, cognitive modelling, problem solving mechanisms, etc. These different perspectives are complementary, each one adding a piece to the puzzle.

This book introduces a new logic-based multi-paradigm programming language that integrates logic programming, functional programming, dynamic programming with tabling, and scripting, for use in solving combinatorial search problems, including CP, SAT, and MIP (mixed integer programming) based solver modules, and a module for planning that is implemented using tabling. The book is useful for undergraduate and graduate students, researchers, and practitioners.

Constraints are everywhere: most computational problems can be described in terms of restrictions imposed on the set of possible solutions, and constraint programming is a problem-solving technique that works by incorporating those restrictions in a programming environment. It draws on methods from combinatorial optimisation and artificial intelligence, and has been successfully applied in a number of fields from scheduling, computational biology, finance, electrical engineering and operations research through to numerical analysis. This textbook for upper-division students provides a thorough and structured account of the main aspects of constraint programming. The author provides many worked examples that illustrate the usefulness and versatility of this approach to programming, as well as many exercises throughout the book that illustrate techniques, test skills and extend the text. Pointers to current research, extensive historical and bibliographic notes, and a comprehensive list of references will also be valuable to professionals in computer science and artificial intelligence.

Constraints; Simplification, optimization and implication; Finite constraint domains; Constraint logic programming; Simple modeling; Using data structures; Controlling search; Modelling with finite domain constraints; Advanced programming techniques; CLP systems; Other constraint programming languages; Constraint databases; Index.

Constraint Programming aims at solving hard combinatorial problems, with a computation time increasing in practice exponentially. The methods are today efficient enough to solve large industrial problems, in a generic framework. However, solvers are dedicated to a single variable type: integer or real. Solving mixed problems relies on ad hoc transformations. In another field, Abstract Interpretation offers tools to prove program properties, by studying an abstraction of their concrete semantics, that is, the set of possible values of the variables during an execution. Various representations for these abstractions have been proposed. They are called abstract domains. Abstract domains can mix any type of variables, and even represent relations between the variables. In this work, we define abstract domains for Constraint Programming, so as to build a generic solving method, dealing with both integer and real variables. We also study the octagons abstract domain, already defined in Abstract Interpretation. Guiding the search by the octagonal relations, we obtain good results on a continuous benchmark. We also define our solving method using Abstract Interpretation techniques, in order to include existing abstract domains. Our solver, AbSolute, is able to solve mixed problems and use relational domains. - Exploits the over-approximation methods to integrate AI tools in the methods of CP - Exploits the relationships captured to solve continuous problems more effectively - Learn from the developers of a solver capable of handling practically all abstract domains