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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.
Constraint satisfaction toolkits are software libraries for imperative programming languages that are used to encode and solve a constraint satisfaction problem. Cassowary constraint solver, an open source project for constraint satisfaction (accessible from C, Java, Python and other languages). Comet, a commercial programming language and toolkit
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]
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 ...
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
Universal algebra provides a natural language for the constraint satisfaction problem (CSP). CSP refers to an important class of computational problems where, given a relational algebra A and an existential sentence φ {\displaystyle \varphi } over this algebra, the question is to find out whether φ {\displaystyle \varphi } can be satisfied in A .
As a result, the constraint satisfaction problem can be used to set a constraint whose relation is the table on the right, which may not be in the constraint language. As a result, if a constraint satisfaction problem has the table on the left as its set of solutions, every relation can be expressed by projecting over a suitable set of variables.
The general constraint satisfaction problem consists in finding a list of integers x = (x[1], x[2], …, x[n]), each in some range {1, 2, …, m}, that satisfies some arbitrary constraint (Boolean function) F. For this class of problems, the instance data P would be the integers m and n, and the predicate F.