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arXiv · 1504.01145

Dualization in Lattices Given by Ordered Sets of Irreducibles

Mikhail A. Babin·Sergei O. Kuznetsov
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Abstract

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal context). We show that in this case dualization is equivalent to the enumeration of so-called minimal hypotheses. In contrast to usual dualization setting, where a lattice is given by the ordered set of its elements, dualization in this case is shown to be impossible in output polynomial time unless P = NP. However, if the lattice is distributive, dualization is shown to be possible in subexponential time.

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Mikhail A. Babin, Sergei O. Kuznetsov. 2015-04-05. Dualization in Lattices Given by Ordered Sets of Irreducibles. https://arxiv.org/abs/1504.01145

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