this paper appeared in the 27th International Colloquium on Automata, Languages and Programming (ICALP'2000). Address: Department of Computer Science, 6 King's College Road, University of Toronto, Ontario M5S 3H5, Canada, email: libkin@cs.toronto.edu. Research aliation: Bell Laboratories

Constraint solving in dynamic environments requires an immediate adaptation of the solutions if the constraint problems are changing. After any change the solutions have to be immediately adapted. Therefore, a wide range of incremental constraint solving algorithms for dynamic constraint satisfaction problems (DCSPs) are available. Some of these algorithms are based on Fruhwirth's Constraint Handling Rules (CHRs) which are rules to implement constraint solvers. Thus, adaptive constraint solving in dynamic environments is generally supported. In this paper, some projection algorithms are presented to eliminate local variables, which are introduced during constraint processing with CHRs. An early projection within each rule application eliminates irrelevant variable bindings while keeping the processed constraint stores quite small. Consequently, the modifications that are required for an adaptation after constraint additions or deletions are reduced. This may result in an ...