Join-Irreducible Boolean Functions

Author： Bouaziz Moncef  

Publisher： Springer Publishing Company

ISSN： 0167-8094

Source： Order, Vol.27, Iss.3, 2010-11, pp. : 261-282

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Abstract

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset $tilde{Omega}$ . Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of $tilde{Omega}$ are the − 2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of $tilde{Omega}$ .

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