Constraint Satisfaction , Constraint Programming

Recently constraint satisfaction has been embedded in various high-level declarative programming environments, like the Constraint Logic Programming framework, and even more recently such environments have been extended with concurrency, like in the Concurrent Constraint Programming paradigm. The merging of diierent areas of research is always an exciting event, and proliic of new ideas. We believe that here it is particularly so, since the above areas, while apparently very far in aims and techniques, are found more and more interconnected, to the point that their coexistence leads to new unexpected directions of research. In fact, we believe that interesting results in constraint satisfaction and in constraint programming can be mixed with concurrency with the consequence that more concurrency, as well as a more natural view of constraint programming, are derived. 1 Organization of the paper In Section 2 we describe our general scheme for local consistency techniques for nite domain constraint problems, together with a speciic eecient instance of the scheme. Then in Section 3 we show how to embed such an instance within the Constraint Logic Programming framework and we discuss its eeciency. In Section 4 we deene, in terms of graph rewriting, a concurrent abstract machine for Concurrent Constraint programs, and we describe how to obtain a suitable semantics which is able to show all the concurrency and the nondeterminism contained in a program. Moreover, we show how to exploit it to derive useful information about the causal dependency of the objects involved in the computations, and we give an example of its application to the automatic parallelization of CLP programs. Finally, we give some suggestions for further research. The presentation is rather informal. Due to the lack of space, we chose to convey the main motivations, ideas, and results instead of writing the technical development. However, the formal details can be found in Ros93] and in the various papers cited throughout the text. Constraint satisfaction problems are very useful for describing many real-life problems, like scene labelling, graph coloring, VLSI routing, hardware design, software speciication and design, and operation research problems. In particular, nite domain constraint problems are signiicantly easier to treat than general ones, and nevertheless are suuciently descriptive of many real situations. Therefore the growing interest in such problems is widely justiied. A ((nite domain) constraint problem can be speciied by giving a set of variables and a set of constraints, where each constraint connects only …