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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
The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. [1] COP is a CSP that includes an objective function to be optimized. Many algorithms are used to handle the optimization part.
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.
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.
SAT itself (tacitly) uses only ∃ quantifiers. If only ∀ quantifiers are allowed instead, the so-called tautology problem is obtained, which is co-NP-complete. If any number of both quantifiers are allowed, the problem is called the quantified Boolean formula problem (QBF), which can be shown to be PSPACE-complete. It is widely believed that ...
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.
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