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Constraint programming is a paradigm for solving computational problems that involves expressing them as a set of constraints. The constraint programming paradigm was first proposed in the 1980s and has since been applied to a wide range of problem domains. The basic idea is to define a search space of potential solutions to a problem and then to apply a set of constraints that rule out those solutions that do not satisfy the requirements of the problem.

A constraint is a statement about a variable, indicating a condition that must be met. For example, in a scheduling problem, a constraint might state that a certain job must be completed within a certain time limit. The constraint programming approach is based on the idea that all problem constraints are modeled as a whole, not separately. This makes it easier to specify and modify the problem.

The constraints are then used to guide the search process, determining which solutions are worth exploring and which should be discarded. The search process typically involves using a combination of search and propagation to iteratively reduce the search space until a solution is found. Methods for propagating constraints include constraint propagation, propagation by look-ahead, and hybrid propagation.

The constraint programming paradigm is widely used in various application domains, such as artificial intelligence, machine learning, scheduling, planning, and optimization. Its ability to model complex problems efficiently makes it a popular choice. Studies have shown that constraint programming can produce good results for certain problem-solving tasks, but its efficiency can be affected by the size and complexity of the problem, as well as the choice of search strategy.