A Fixpoint Definition of Dynamic Constraint Satisfaction

Abstract

Many combinatorial problems can be represented naturally as constraint satisfaction problems (CSP). However, in some domains the set of variables in a solution should change dynamically on the basis of assignments of values to variables. In this paper we argue that such dynamic constraint satisfaction problems (DCSP), introduced by Mittal and Falkenhainer, are more expressive than CSP in a knowledge representation sense. We then study the problem of generalizing the original DCSP with disjunctive activity constraints and default negation which are useful in, e.g., product configuration problems. The generalization is based on a novel definition of a solution to DCSP. It uses a fixpoint condition instead of the subset minimality condition in the original formulation. Our approach coincides with the original definition when disjunctions and default negations are not allowed. However, it leads to lower computational complexity than if the original definition were generalized similarly. In fact we show that the generalized DCSP is NP-complete. As a proof of concept, we briefly describe two novel implementations of the original DCSP and give test results for them.