Computing Resolution-Path Dependencies in Linear Time ,

  • Friedrich Slivovsky
  • Stefan Szeider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7317)


The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for representing such dependencies. Since it is generally intractable to determine dependencies exactly, a set of potential dependencies is computed instead, which may include false positives. Among the schemes proposed so far, resolution path dependencies introduce the fewest spurious dependencies. In this work, we describe an algorithm that detects resolution-path dependencies in linear time, resolving a problem posed by Van Gelder (CP 2011).


Linear Time Binary Relation Boolean Formula Blue Edge Dependency Pair 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Friedrich Slivovsky
    • 1
  • Stefan Szeider
    • 1
  1. 1.Institute of Information SystemsVienna University of TechnologyViennaAustria

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