Abstract
A quantified Boolean formula is true, if for any existentially quantified variable there exists a Boolean function depending on the preceding universal variables, such that substituting the existential variables by the Boolean functions results in a true formula. We call a satisfying set of Boolean functions a model. In this paper, we investigate for various classes of quantified Boolean formulas and various classes of Boolean functions the problem whether a model exists. Furthermore, for these classes the complexity of the model checking problem – whether a set of Boolean functions is a model for a formula – will be shown. Finally, for classes of Boolean functions we establish some characterizations in terms of quantified Boolean formulas which have such a model. For example, roughly speaking any satisfiable quantified Boolean Horn formula can be satisfied by monomials and vice versa.
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Büning, H.K., Zhao, X. (2004). On Models for Quantified Boolean Formulas. In: Lenski, W. (eds) Logic versus Approximation. Lecture Notes in Computer Science, vol 3075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25967-1_3
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DOI: https://doi.org/10.1007/978-3-540-25967-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22562-1
Online ISBN: 978-3-540-25967-1
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