Basic characteristics of constraint programming

THIS BOOK IS about constraint programming, an alternative approach to programming which relies on a combination of techniques that deal with reasoning and computing. It has been successfully applied in a number of fields including molecular biology, electrical engineering, operations research and numerical analysis. The central notion is that of a constraint. Informally, a constraint on a sequence of variables is a relation on their domains. It can be viewed as a requirement that states which combinations of values from the variable domains are admitted. In turn, a constraint satisfaction problem consists of a finite set of constraints, each on a subsequence of a given sequence of variables.

To solve a given problem by means of constraint programming we first formulate it as a constraint satisfaction problem. To this end we

• introduce some variables ranging over specific domains and constraints over these variables;

• choose some language in which the constraints are expressed (usually a small subset of first-order logic).

This part of the problem solving is called modeling. In general, more than one representation of a problem as a constraint satisfaction problem exists. Then to solve the chosen representation we use either

• domain specific methods,

or

• general methods,

or a combination of both.

The domain specific methods are usually provided in the form of implementations special purpose algorithms.