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An Empirical study of QBF encodings: from treewidth estimation to useful preprocessing

Pulina, Luca and Tacchella, Armando (2010) An Empirical study of QBF encodings: from treewidth estimation to useful preprocessing. Fundamenta Informaticae, Vol. 102 (3-4), p. 391-427. eISSN 1875-8681. Article.

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From an empirical point of view, the hardness of quantified Boolean formulas (QBFs), can be characterized by the (in)ability of current state-of-the-art QBF solvers to decide about the truth of formulas given limited computational resources. In this paper, we start from the problem of computing empirical hardness markers, i.e., features that can discriminate between hard and easy QBFs, and we end up showing that such markers can be useful to improve our understanding of QBF preprocessors. In particular, considering the connection between classes of tractable QBFs and the treewidth of associated graphs, we show that (an approximation of) treewidth is indeed a marker of empirical hardness and it is the only parameter which succeeds consistently in being so, even considering several other purely syntactic candidates which have been successfully employed to characterize QBFs in other contexts. We also show that treewidth approximations can be useful to describe the effect of QBF preprocessors, in that some QBF solvers benefit from a preprocessing phase when it reduces the treewidth of their input. Our experiments suggest that structural simplifications reducing treewidth are a potential enabler for the solution of hard QBF encodings.

Item Type:Article
ID Code:7106
Uncontrolled Keywords:Quantified Boolean formulas (QBFs), computing empirical hardness markers, treewidth estimation
Subjects:Area 09 - Ingegneria industriale e dell'informazione > ING-INF/05 Sistemi di elaborazione delle informazioni
Divisions:001 Università di Sassari > 01 Dipartimenti > Economia, istituzioni e società
Publisher:IOS Press
Deposited On:14 Feb 2012 10:59

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