English

A Strongly Exponential Separation of DNNFs from CNF Formulas

Computational Complexity 2015-02-20 v3

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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Cite

@article{arxiv.1411.1995,
  title  = {A Strongly Exponential Separation of DNNFs from CNF Formulas},
  author = {Simone Bova and Florent Capelli and Stefan Mengel and Friedrich Slivovsky},
  journal= {arXiv preprint arXiv:1411.1995},
  year   = {2015}
}