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Nested Boolean Functions as Models for Quantified Boolean Formulas

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Theory and Applications of Satisfiability Testing – SAT 2013 (SAT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7962))

Abstract

Nested Boolean functions or Boolean programs are an alternative to the quantified Boolean formula (QBF) characterization of polynomial space. The idea is to start with a set of Boolean functions given as propositional formulas and to define new functions as compositions or instantiations of previously defined ones. We investigate the relationship between function instantiation and quantification and present a compact representation of models and countermodels of QBFs with and without free variables as nested Boolean functions. The representation is symmetric with respect to Skolem models and Herbrand countermodels. For a formula with free variables, it can describe both kinds of models simultaneously in one complete equivalence model which can be Skolem or Herbrand depending on actual assignments to the free variables.

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Author information

Authors and Affiliations

  1. Computer Science Institute, University of Paderborn, Germany

    Uwe Bubeck & Hans Kleine Büning

Authors
  1. Uwe Bubeck
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  2. Hans Kleine Büning
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Editor information

Editors and Affiliations

  1. HIIT and Department of Computer Science, University of Helsinki, Gustaf Hällströmin katu 2 b, 00014, Helsinki, Finland

    Matti Järvisalo

  2. Computer Science Department, University of California at Santa Cruz, 1156 High Street, SOE-3, 95064, Santa Cruz, CA, USA

    Allen Van Gelder

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Bubeck, U., Kleine Büning, H. (2013). Nested Boolean Functions as Models for Quantified Boolean Formulas. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_20

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  • DOI: https://doi.org/10.1007/978-3-642-39071-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39070-8

  • Online ISBN: 978-3-642-39071-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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