Bounded-width QBF is PSPACE-complete
Document typeConference report
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Rights accessOpen Access
Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisﬁability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantiﬁed version of SAT. It was shown by Pan and Vardi [LICS 2006] that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded treewidth. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.
CitationAtserias, A.; Oliva, S. Bounded-width QBF is PSPACE-complete. A: Symposium on Theoretical Aspects of Computer Science. "30th International Symposium on Theoretical Aspects of Computer Science : STACS '13, February 27th to March 2nd, 2013, Kiel, Germany". Kiel: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2013, p. 1-11.