On the relation between structured $d$-DNNFs and SDDs
Abstract
Structured -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 -DNNFs. Beame and Liew (2015) as well as Bova and Szeider (2017) mentioned the question whether structured -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 -DNNFs that respect the same vtree.
Cite
@article{arxiv.1912.01430,
title = {On the relation between structured $d$-DNNFs and SDDs},
author = {Beate Bollig and Martin Farenholtz},
journal= {arXiv preprint arXiv:1912.01430},
year = {2020}
}
Comments
16 pages. The main result of the paper generalizes one of the results from paper arXiv:1802.04544 where unambiguous nondeterministic OBDDs are considered which can be seen as restricted structured $d$-DNNFs