Collapsibility and Consistency in Quantified Constraint Satisfaction

The concept of consistency has pervaded studies of the constraint satisfaction problem. We introduce two concepts, which are inspired by consistency, for the more general framework of the quantified constraint satisfaction problem (QCSP). We use these concepts to derive, in a uniform fashion, proofs of polynomial-time tractability and corresponding algorithms for certain cases of the QCSP where the types of allowed relations are restricted. We not only unify existing tractability results and algorithms, but also identify new classes of tractable QCSPs.