Constraint programming: Difference between revisions

Revision as of 15:10, 21 October 2019

Revision as of 15:25, 28 November 2019

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FourThree categories of constraints exist:

* extensional constraints: constraints are defined by enumerating the set of values that would satisfy them;

* arithmetic constraints: constraints are defined by an arithmetic expression, i.e., using <math><, >, \leq, \geq, =, \neq,...</math>;

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{{math theorem

|Definition

| An assignationassignment (or model) <math>\mathcal{A}</math> of a CSP <math>P = (\mathcal{X},\mathcal{D},\mathcal{C})</math> is defined by the couple <math>\mathcal{A} = (\mathcal{X_{\mathcal{A}}}, \mathcal{V_{\mathcal{A}}})</math> where:

* <math>\mathcal{X_{\mathcal{A}}} \subset \mathcal{X} </math> is a subset of variable;

* <math>\mathcal{V_{\mathcal{A}}} = \{ v_{\mathcal{A}_1}, \dots, v_{\mathcal{A}_k}\} \in \{ \mathcal{D}_{\mathcal{A}_1}, \dots, \mathcal{D}_{\mathcal{A}_k}\}</math> is the tuple of the values taken by the assigned variables.

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WeAssignment calledis assignation anthe association of a variable to a value from its ___domain. A partial assignationassignment is when a sub-setsubset of the variables of the problem have been assigned. A total assignationassignment is when all the variables of the problem have been assigned.

{{math theorem