On the relation between structured $d$-DNNFs and SDDs

Beate Bollig; Martin Farenholtz

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arXiv · 1912.01430

On the relation between structured $d$-DNNFs and SDDs

Beate Bollig·Martin Farenholtz

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Abstract

Structured $d$-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs are restricted structured $d$-DNNFs. Beame and Liew (2015) as well as Bova and Szeider (2017) mentioned the question whether structured $d$-DNNFs are really more general than SDDs w.r.t. polynomial-size representations (w.r.t. the number of Boolean variables the represented functions are defined on.) The main result in the paper is the proof that a function can be represented by SDDs of polynomial size if the function and its complement have polynomial-size structured $d$-DNNFs that respect the same vtree.

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Beate Bollig, Martin Farenholtz. 2019-12-02. On the relation between structured $d$-DNNFs and SDDs. https://arxiv.org/abs/1912.01430

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