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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
Every constraint satisfaction problem and subset of its variables defines a relation, which is composed by all tuples of values of the variables that can be extended to the other variables to form a solution. Technically, this relation is obtained by projecting the relation having the solutions as rows over the considered variables.
Constraint propagation in constraint satisfaction problems is a typical example of a refinement model, and formula evaluation in spreadsheets are a typical example of a perturbation model. The refinement model is more general, as it does not restrict variables to have a single value, it can lead to several solutions to the same problem.
AC-3 operates on constraints, variables, and the variables' domains (scopes). A variable can take any of several discrete values; the set of values for a particular variable is known as its domain. A constraint is a relation that limits or constrains the values a variable may have. The constraint may involve the values of other variables.
Decomposition methods create a problem that is easy to solve from an arbitrary one. Each variable of this new problem is associated to a set of original variables; its domain contains tuples of values for the variables in the associated set; in particular, these are the tuples that satisfy a set of constraints over these variables.
If the problem mandates that the constraints be satisfied, as in the above discussion, the constraints are sometimes referred to as hard constraints.However, in some problems, called flexible constraint satisfaction problems, it is preferred but not required that certain constraints be satisfied; such non-mandatory constraints are known as soft constraints.
The soft satisfiability problem (soft-SAT), given a set of SAT problems, asks for the maximum number of those problems which can be satisfied by any assignment. [16] The minimum satisfiability problem. The MAX-SAT problem can be extended to the case where the variables of the constraint satisfaction problem belong to the set