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Backdoor Sets of Quantified Boolean Formulas

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Abstract

We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two important tractable classes. In contrast to known tractable classes based on bounded treewidth, the number of quantifier alternations of our classes is unbounded. As a side product of our considerations we develop a theory of variable dependency which is of independent interest.

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Authors and Affiliations

  1. TU Darmstadt, Darmstadt, Germany

    Marko Samer

  2. University of Durham, Durham, UK

    Stefan Szeider

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  1. Marko Samer
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  2. Stefan Szeider
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Correspondence to Marko Samer.

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Samer, M., Szeider, S. Backdoor Sets of Quantified Boolean Formulas. J Autom Reasoning 42, 77–97 (2009). https://doi.org/10.1007/s10817-008-9114-5

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