Antichain-Based QBF Solving

  • Thomas Brihaye
  • Véronique Bruyère
  • Laurent Doyen
  • Marc Ducobu
  • Jean-Francois Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6996)


We consider the problem of QBF solving viewed as a reachability problem in an exponential And-Or graph. Antichain-based algorithms for reachability analysis in large graphs exploit certain subsumption relations to leverage the inherent structure of the explored graph in order to reduce the effect of state explosion, with high performance in practice.

In this paper, we propose simple notions of subsumption induced by the structural properties of the And-Or graphs for QBF solving. Subsumption is used to reduce the size of the search tree, and to define compact representations of certificates (in the form of antichains) both for positive and negative instances of QBF. We show that efficient exploration of the reduced search tree essentially relies on solving variants of Max-SAT and Min-SAT. Preliminary stand-alone experiments of this algorithm show that the antichain-based approach is promising.


Winning Strategy Boolean Formula Binary Decision Diagram Reachability Problem Subsumption Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thomas Brihaye
    • 1
  • Véronique Bruyère
    • 2
  • Laurent Doyen
    • 3
  • Marc Ducobu
    • 1
  • Jean-Francois Raskin
    • 4
  1. 1.Institut de MathématiqueUniversité de MonsBelgique
  2. 2.Institut d’InformatiqueUniversité de MonsBelgique
  3. 3.LSV, ENS Cachan & CNRSFrance
  4. 4.Département d’InformatiqueUniversité Libre de BruxellesBelgique

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