# 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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