Bounded-width QBF is PSPACE-complete

Authors Albert Atserias, Sergi Oliva

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Albert Atserias
Sergi Oliva

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Albert Atserias and Sergi Oliva. Bounded-width QBF is PSPACE-complete. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 44-54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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 tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.
  • Tree-width
  • QBF
  • PSPACE-complete


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