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.
We identify a useful class of logic programs with negation, called stratified programs, that disallow certain combinations of recursion and negation. Programs in this class have a simple declarative and procedural meaning based, respectively, on model theory and a back-chaining interpreter. The standard model of a stratified program, which gives the program a declarative meaning and is independent of the stratification, is characterized in two ways. One is based on a fixed point theory of nonmonotonic operators and the other on an abstract declarative characterization. The back-chaining interpreter also determines the standard model. Finally, we prove the consistency of Clark's completion for stratified programs and attempt to clarify the sources of some previously reported difficulties with negation in logic programming.
We propose an abstract approach to coalition formation that focuses on simple merge and split rules transforming partitions of a group of players. We identify conditions under which every iteration of these rules yields a unique partition. The main conceptual tool is a specific notion of a stable partition. The results are parametrized by a preference relation between partitions of a group of players and naturally apply to coalitional TU-games, hedonic games and exchange economy games.
A survey of various results concerning Hoare's approach to proving partial and total correctness of programs is presented. Emphasis is placed on the soundness and completeness issues. Various proof systems for while programs, recursive procedures, local variable declarations, and procedures with parameters, together with the corresponding soundness, completeness, and incompleteness results, are discussed.
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