Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dualization in Lattices Given by Ordered Sets of Irreducibles   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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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con