Disjoint essential sets of implicates of a CQ Horn function

Authors:
Ondřej Čepek;Petr Kučera
Affiliations:
Department of Theoretical Computer Science and Mathematical Logic, Charles University, Praha 1, Czech Republic 118 00 and Institute of Finance and Administration - VŠFS, Praha 10, Czech Repub ...;Department of Theoretical Computer Science and Mathematical Logic, Charles University, Praha 1, Czech Republic 118 00
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2011

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Abstract

In this paper we study a class of CQ Horn functions introduced in聽Boros et聽al.聽(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.