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arXiv · 1811.09435

Backdoor Decomposable Monotone Circuits and their Propagation Complete Encodings

Petr Kučera·Petr Savický
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Abstract

We describe a compilation language of backdoor decomposable monotone circuits (BDMCs) which generalizes several concepts appearing in the literature, e.g. DNNFs and backdoor trees. A $\mathcal{C}$-BDMC sentence is a monotone circuit which satisfies decomposability property (such as in DNNF) in which the inputs (or leaves) are associated with CNF encodings from a given base class $\mathcal{C}$. We consider the class of propagation complete (PC) encodings as a base class and we show that PC-BDMCs are polynomially equivalent to PC encodings. Additionally, we use this to determine the properties of PC-BDMCs and PC encodings with respect to the knowledge compilation map including the list of efficient operations on the languages.

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Petr Kučera, Petr Savický. 2018-11-23. Backdoor Decomposable Monotone Circuits and their Propagation Complete Encodings. https://arxiv.org/abs/1811.09435

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