On Dualization over Distributive Lattices

@article{Elbassioni2020OnDO,
title={On Dualization over Distributive Lattices},
author={Khaled M. Elbassioni},
journal={ArXiv},
year={2020},
volume={abs/2006.15337}
}
Given a partially order set (poset) $P$, and a pair of families of ideals $\mathcal{I}$ and filters $\mathcal{F}$ in $P$ such that each pair $(I,F)\in \mathcal{I}\times\mathcal{F}$ has a non-empty intersection, the dualization problem over $P$ is to check whether there is an ideal $X$ in $P$ which intersects every member of $\mathcal{F}$ and does not contain any member of $\mathcal{I}$. Equivalently, the problem is to check for a distributive lattice $L=L(P)$, given by the poset $P$ of its set…

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