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Backdoor Sets of Quantified Boolean Formulas

  • Marko Samer
  • Stefan Szeider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4501)

Abstract

We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas in conjunctive normal form (QCNF). We develop parameterized algorithms that admit uniform polynomial time QCNF evaluation parameterized by the size of smallest strong backdoor sets. For our algorithms we develop a theory of variable dependency which is of independent interest. As a result, we obtain hierarchies of classes of tractable QCNF formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two prominent tractable classes. In contrast to known tractable classes based on bounded treewidth, the number of quantifier alternations of our classes is unbounded.

Keywords

Polynomial Time Tractable Classis Conjunctive Normal Form Truth Assignment Boolean Formula 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Marko Samer
    • 1
  • Stefan Szeider
    • 1
  1. 1.Department of Computer Science, Durham UniversityUK

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