Hybrid Tractable Classes of Binary Quantified Constraint Satisfaction Problems

As a central problem in AI, the Constraint Satisfaction Problem (CSP), has been a popular paradigm to cope with complex combinational problems. A CSP consists of a set of variables and a set of constraints restricting the combinations of values taken by variables. The Quantified Constraint Satisfaction Problem (QCSP) is a generalization of the CSP, where variables are existentially or universally quantified. It is well-known that deciding the satisfiability of CSPs is NP-complete, while QCSPs have been proved to be PSPACE-complete. Hence, a great amount of attention has been drawn on identifying polynomial-time tractable classes of them. There are three main kinds of tractable classes for CSPs: structural classes; relational classes; hybrid classes (Dechter 2003). Many structural and relational tractable classes of QCSPs have been reported (Chen 2004; Gottlob, Greco, and Scarcello 2005), but there is little attention on hybrid tractable classes for QCSPs, which have achieved great success on CSPs (van Beek and Dechter 1995; Zhang and Freuder 2008; Cooper, Jeavons, and Salamon 2010). In this paper, we first identity a hybrid tractable class of QCSPs with the Broken-Triangle Property (BTP) (Cooper, Jeavons, and Salamon 2010), and then propose the broken-angle property for QCSPs to deal with the case that the variable ordering of the BTP differs from the ordering in the prefix, and thus identify a new tractable class. Next, we show that the property of min-of-max extensibility, a generalization of the BTP, can also be used to identify tractable classes of QCSPs in a similar way.