Minimal False Quantified Boolean Formulas

  • Hans Kleine Büning
  • Xishun Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4121)


This paper is concerned with the minimal falsity problem MF for quantified Boolean formulas. A QCNF formula (i.e., with CNF-matrix) is called minimal false, if the formula is false and any proper subformula is true. It is shown that the minimal falsity problem is PSPACE-complete. Then the deficiency of a QCNF formula is defined as the difference between the number of clauses and the number of existentially quantified variables. For quantified Boolean formulas with deficiency one, MF is solvable in polynomial time.


Polynomial Time Induction Hypothesis Truth Assignment Boolean Formula Propositional Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hans Kleine Büning
    • 1
  • Xishun Zhao
    • 2
  1. 1.Department of Computer ScienceUniversität PaderbornPaderbornGermany
  2. 2.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouP.R. China

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