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- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer Science+Business Media B.V.
- Subject
- Computer Science; Mathematics, general; Artificial Intelligence (incl. Robotics); Statistical Physics, Dynamical Systems and Complexity; Computer Science, general
- ISSN
- 1012-2443
- eISSN
- 1573-7470
- DOI
- 10.1007/s10472-011-9263-9
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we study a class of CQ Horn functions introduced in Boros et al. (Ann Math Artif Intell 57(3–4):249–291, 2010). We prove that given a CQ Horn function f, the maximal number of pairwise disjoint essential sets of implicates of f equals the minimum number of clauses in a CNF representing f. In other words, we prove that the maximum number of pairwise disjoint essential sets of implicates of f constitutes a tight lower bound on the size (the number of clauses) of any CNF representation of f.
Journal
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Nov 12, 2011