A Strongly Exponential Separation of DNNFs from CNF Formulas

Simone Bova; Florent Capelli; Stefan Mengel; Friedrich Slivovsky

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arXiv · 1411.1995

A Strongly Exponential Separation of DNNFs from CNF Formulas

Simone Bova·Florent Capelli·Stefan Mengel·Friedrich Slivovsky

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Abstract

Decomposable Negation Normal Forms (DNNFs) are Boolean circuits in negation normal form where the subcircuits leading into each AND gate are defined on disjoint sets of variables. We prove a strongly exponential lower bound on the size of DNNFs for a class of CNF formulas built from expander graphs. As a corollary, we obtain a strongly exponential separation between DNNFs and CNF formulas in prime implicates form. This settles an open problem in the area of knowledge compilation (Darwiche and Marquis, 2002).

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Simone Bova, Florent Capelli, Stefan Mengel, Friedrich Slivovsky. 2014-11-07. A Strongly Exponential Separation of DNNFs from CNF Formulas. https://arxiv.org/abs/1411.1995

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