Four subareas of the theory of constraints, and their links

Abstract

Let V={x1,...,xn} be a set of variables that range over a set of values D {d1,...,dq}. A constraint is an expression of the type , where R⊆Dr is a relation on the domain set D and are variables in V. The space of assignments, or configurations, is the set of all mappings σ: V →D. We say that σ satisfies the constraint R(xi1, . . . , xir) if(σ(xi1 ), . . . ,σ(xir )) ∈ R. Otherwise we say that it falsifies it. On a given system of constraints we face a number of important computational problems. © 2009 Springer Berlin Heidelberg.