Quantified Boolean Formulas (QBFs) enable standard representation of PSPACE problems. In particular, formulas with two quantifier levels (2QBFs) enable representing problems in the second level of the polynomial hierarchy (Π2 P , Σ2 P ). This paper proposes an algorithm for solving 2QBF satisfiability by counterexample guided abstraction refinement (CEGAR). This represents an alternative approach to 2QBF satisfiability and, by extension, to solving decision problems in the second level of polynomial hierarchy. In addition, the paper presents a comparison of a prototype implementing the presented algorithm to state of the art QBF solvers, showing that a larger set of instances is solved.


Model Check Conjunctive Normal Form Boolean Formula Bound Model Check Conjunctive Normal Form Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mikoláš Janota
    • 2
  • Joao Marques-Silva
    • 1
    • 2
  1. 1.University College DublinIreland
  2. 2.INESC-IDLisbonPortugal

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