Encoding global constraints in semiring-based constraint solving

In recent work, a general framework for constraint satisfaction over finite domains has been proposed, based on the concept of semiring-valued constraints. Classical CSPs, fuzzy CSPs, and hierachical CSPs can be easily cast in this general framework. In this paper, we claim that translating any constraint problem into a semiring-based constraint problem makes it possible to express global information about the problem more easily, especially in the case of non-crisp or preference constraints. Applying this concept to the case of set-based semirings, we give a theoretical result and two practical applications developed using clp(FD, S), a full and efficient implementation of semiring-based constraint satisfaction in the CLP paradigm