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Boolean Functions as Models for Quantified Boolean Formulas

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Abstract

In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whether a given set of Boolean functions is a model for a formula. For classes of Boolean functions, we establish some characterizations in terms of classes of quantified Boolean formulas that have such a model.

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Authors and Affiliations

  1. Department of Computer Science, Universität Paderborn, 33095, Paderborn, Germany

    Hans Kleine Büning

  2. LDCSEE, West Virginia University, Morgantown, WV, 26506, USA

    K. Subramani

  3. Institute of Logic and Cognition, Sun Yat-sen University, 510275, Guangzhou, People’s Republic of China

    Xishun Zhao

Authors
  1. Hans Kleine Büning
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  2. K. Subramani
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  3. Xishun Zhao
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Corresponding author

Correspondence to Hans Kleine Büning.

Additional information

This research has been supported in part by the Air Force Office of Scientific Research under grant FA9550-06-1-0050.

This research has been supported in part by the NSFC under grants 60573011 and 10410638.

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Kleine Büning, H., Subramani, K. & Zhao, X. Boolean Functions as Models for Quantified Boolean Formulas. J Autom Reasoning 39, 49–75 (2007). https://doi.org/10.1007/s10817-007-9067-0

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  • DOI: https://doi.org/10.1007/s10817-007-9067-0

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