Equivalence in QCSP (QBF)

The QBF validity problem with any propositional formulamay be seen as a QCSP. In this frame, we introduce a new constraint: the equivalence constraint and prove that it is stronger than equality constraint. In order to design this equivalence constraint, we introduce a new sequent calculus for QBF which is based on an equivalence relation over subformulae. This sequent calculus is proven to be sound and complete w.r.t. the semantics of the QBF. Based on this system, we define our equivalence constraint in such a way that QCSP(QBF) may be seen as a CSP(QBF) with a quantied search algorithm. We report some experiments in a generic constraint development environment

The cut tool for QCSP

Quantified Constraint Satisfaction Problems (QCSP) are a generalization of Constraint Satisfaction Problems (CSP) in which variables may be quantified existentially and universally. QCSP offers a natural framework to express PSPACE problems as finite two-player games or planning under uncertainty. State-of-the-art QCSP solvers have an important drawback: they explore much larger combinatorial spaces than the natural search space of the original problem since they are unable to recognize that some sub-problems are necessarily true. We introduce a new tool, inspired by the cut rule of Prolog as a tool under responsibility of the designer of the QCSP, to prune those parts of the search space which are by construction known to be useless. We use this new tool to restore on one hand the annihilator property of true for disjunction in QCSP solver and, on the other hand, to prune the search space in two-player games. It is a simple solution to use efficiently QCSP to design finite two-player games without restricting the QCSP language. This tool does not need to modify the QCSP solver but has only one requirement: be able to tell the QCSP solver that the current QCSP is solved. Our QCSP solver built over Ge Code, a CSP library, obtained very good results compared to state-of-the-art QCSP solvers

Quantified Constraint Handling Rules

We shift the QCSP (Quantified Constraint Satisfaction Problems) framework to the QCHR (Quantified Constraint Handling Rules) framework by enabling dynamic binder and access to user-defined constraints. QCSP offers a natural framework to express PSPACE problems as finite two-players games. But to define a QCSP model, the binder must be formerly known and cannot be built dynamically even if the worst case won\u27t occur. To overcome this issue, we define the new QCHR formalism that allows to build the binder dynamically during the solving. Our QCHR models exhibit state-of-the-art performances on static binder and outperforms previous QCSP approaches when the binder is dynamic