Extended Failed-Literal Preprocessing for Quantified Boolean Formulas

  • Allen Van Gelder
  • Samuel B. Wood
  • Florian Lonsing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7317)


~Building on recent work that adapts failed-literal analysis (FL) to Quantified Boolean Formulas (QBF), this paper introduces extended failed-literal analysis (EFL). FL and EFL are both preprocessing methods that apply a fast, but incomplete reasoning procedure to abstractions of the underlying QBF. EFL extends FL by remembering certain binary clauses that are implied by the same reasoning procedure as FL when it assumes one literal and that implies a second literal. This extension is almost free because the second literals are implied anyway during FL, but compared to analogous techniques for propositional satisfiability, its correctness involves some subtleties. For the first time, application of the universal pure literal rule is considered without also applying the existential pure literal rule. It is shown that using both pure literal rules in EFL is unsound. A modified reasoning procedure for QBF, called Unit-clause Propagation with Universal Pure literals (UPUP) is described and correctness is proved for EFL based on UPUP. Empirical results on the 568-benchmark suite of QBFEVAL-10 are presented.


quantified boolean formulas QBF failed literals extended failed literals 1-saturation look-ahead preprocessing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Allen Van Gelder
    • 1
  • Samuel B. Wood
    • 1
  • Florian Lonsing
    • 2
  1. 1.University of CaliforniaSanta CruzUSA
  2. 2.Johannes Kepler UniversityAustria

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