Typical real world tasks such as configuration or design exhibit dynamic aspects which require extending the basic constraint satisfaction framework. In this paper we use the notion of conditional constraint satisfaction (CondCSP) as defined by [ Mittal and Falkenhainer, 1990 ] to provide a framework in which these problems can be formulated and solved. It has been shown in [ Soininen et al., 1999 ] that the decision problem for CondCSP is NP -complete similar to standard CSPs. Solving standard CSPs applies various degrees of local consistency to avoid recomputing infeasible branches in the search tree. In a similar manner, we define new types of local consistency aimed at solving conditional CSPs more e#ciently. The di#erent algorithms are compared using a series of randomly generated problems.

Conditional Constraint Satisfaction Problems (CC-SPs) are generalizations of classical CSPs that support conditional activation of variables and constraints. Despite the interest emerged for CCSPs in the context of modelling the intrinsic dynamism of diagnosis, structural design, and product configuration applications, a complete characterization of their computational properties and of their expressiveness is still missing. In fact, the aim of the paper is precisely to face these open research issues. First, CCSPs are formally characterized in terms of a suitable fragment of first-order logic. Second, the complexity of some basic reasoning tasks for CC-SPs is studied, by establishing completeness results for the first and the second level of the polynomial hierarchy. Finally, motivated by the hardness results, an island of tractability for CCSPs is identified, by extending structural decomposition methods originally proposed for CSPs. 1

Abstract. In this paper we introduce a modeling approach of the design process of customizations, based on a Model of Abstractions from the Product (MAP). Although variables and constraints are elements of a MAP, this approach differs from other approaches related to CSP in the way values are assigned to the variables, with major implications to the instantiation process. By this approach, product customizations in which components have to be designed to meet the customer specifications can also be dealt with. 1