{"type":"ScholarlyArticle","title":"The Complexity of Quantified Constraint Satisfaction Problems under Structural Restrictions","authors":[{"name":"Georg Gottlob","slug":"georg-gottlob","given":"Georg","family":"Gottlob","affiliation":""},{"name":"Gianluigi Greco","slug":"gianluigi-greco","given":"Gianluigi","family":"Greco","affiliation":""},{"name":"Francesco Scarcello","slug":"francesco-scarcello","given":"Francesco","family":"Scarcello","affiliation":""}],"abstract":"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 ∃∀ 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.","doi":null,"url":"https://ijcai.org/proceedings/2005/148","pdf":"https://ijcai.org/proceedings/2005/0148.pdf","markdown":"https://ijcai.org/proceedings/2005/148.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/148","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":148,"pages":{"first":150,"last":154},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}