Formal Definition
Formally, a constraint satisfaction problem is defined as a triple, where is a set of variables, is a domain of values, and is a set of constraints. Every constraint is in turn a pair (usually represented as a matrix), where is an -tuple of variables and is an -ary relation on . An evaluation of the variables is a function from the set of variables to the domain of values, . An evaluation satisfies a constraint if . A solution is an evaluation that satisfies all constraints.
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