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Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.
Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm. Constraint satisfaction as a general problem originated in the field of artificial intelligence in the 1970s (see for example (Laurière 1978)).
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. [1]
An example constraint satisfaction problem; this problem is binary, and the constraints are represented by edges of this graph. A decomposition tree; for every edge of the original graph, there is a node that contains both its endpoints; all nodes containing a variable are connected
A constraint is composed of a sequence of variables, called its scope, and a set of their evaluations, which are the evaluations satisfying the constraint. The constraint satisfaction problems referred to in this article are assumed to be in a special form.
[3] [4] In modern terms, the problem SAT(S) is viewed as a constraint satisfaction problem over the Boolean domain. In this area, it is standard to denote the set of relations by Γ and the decision problem defined by Γ as CSP(Γ). This modern understanding uses algebra, in particular, universal algebra. For Schaefer's dichotomy theorem, the ...
In constraint satisfaction, constraint inference is a relationship between constraints and their consequences. A set of constraints D {\displaystyle D} entails a constraint C {\displaystyle C} if every solution to D {\displaystyle D} is also a solution to C {\displaystyle C} .
where () = =, …, and () =, …, are constraints that are required to be satisfied (these are called hard constraints), and () is the objective function that needs to be optimized subject to the constraints. In some problems, often called constraint optimization problems, the objective function is actually the sum of cost functions, each of ...