Resolution for quantified Boolean formulas
Information and Computation
Closure properties of constraints
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
Constraint Processing
Collapsibility and consistency in quantified constraint satisfaction
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Variable Dependencies of Quantified CSPs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Treewidth: A Useful Marker of Empirical Hardness in Quantified Boolean Logic Encodings
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A structural approach to reasoning with quantified Boolean formulas
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Tree-width for first order formulae
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Learning to integrate deduction and search in reasoning about quantified boolean formulas
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
An Empirical Study of QBF Encodings: from Treewidth Estimation to Useful Preprocessing
Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Collapsibility in infinite-domain quantified constraint satisfaction
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Decomposing Quantified Conjunctive (or Disjunctive) Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Block-Sorted quantified conjunctive queries
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We give a clear picture of the tractability/intractability frontier for quantified constraint satisfaction problems (QCSPs) under structural restrictions. On the negative side, we prove that checking QCSP satisfiability remains PSPACE-hard for all known structural properties more general than bounded treewidth and for the incomparable hypergraph acyclicity. Moreover, if the domain is not fixed, the problem is PSPACE-hard even for tree-shaped constraint scopes. On the positive side, we identify relevant tractable classes, including QCSPs with prefix Æ having bounded hypertree width, and QCSPs with a bounded number of guards. The latter are solvable in polynomial time without any bound on domains or quantifier alternations.