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Статья

Dualization in lattices given by ordered sets of irreducibles

Theoretical Computer Science. 2017. Vol. Volume 658, Part B. No. 7 January. P. 316-326.
Babin M. A., Kuznetsov S. O.

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 values 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.