Constraint Reductions

It is not usual to be asked to write something on a subject on which you have worked fifteen years before and on which you have remained far from subsequent developments. Yet this is the challenge we humbly accepted to undertake in this paper with the limitation that our expertise in this research area have diminished regarding the developments made by many others during the ten previous years. We begin with the easy part consisting in recalling the context of the paper [BB03]. In the sequel the word constraint will be used in two meanings: a type of constraints, such as propositional clause, Boolean cardinality constraint, ALLDIFF..., and a constraint instance, i.e., the formal representation of a relation on several variables each having a domain. We will use the word Constraint in the first case and constraint in the second case.