Introduction to the special issue on quantified CSPs and QBF

Constraint satisfaction problems (CSPs) and satisfiability problem (SAT) are very successful frameworks that are used to model and solve a wide variety of combinatorial problems. However, there are classes of problems containing uncertainty that arise in areas such as contingent planning, adversarial game playing, control design, and model checking that cannot be expressed within these frameworks. Typically, such problems involve decisions or events that are beyond the control of the problem solving agent and thus cannot be handled using standard (existentially quantified) variables. Quantified CSPs and quantified Boolean formulae (QBF), which are the extensions of CSPs and SAT that allow for universally quantified variables, make it possible to model and reason with such problems, as well as other problems that contain “bounded uncertainty”. As a result, these frameworks have been attracting significant interest in recent years. The main advances have been achieved in the area of QBF where numerous solvers have been implemented and real problems of considerable size have been tackled. There is also a significant body of work on quantified numerical constraints over continuous domains, while research works on quantified constraint satisfaction problems (QCSPs) with discrete finite domains have started to emerge. With this special issue of Constraints we aim to group together and reflect the state of the art in these rapidly developing areas of research. The papers in this special issue concern the three areas of reasoning with quantified constraints highlighted above.