Algorithms for k-meet-semidistributive lattices

International audienceIn this paper we consider k-meet-semidistributive lattices and we are interested in the computation of the set-colored poset associated to an implicational base. The parameter k is of interest since for any finite lattice L there exists an integer k for which L is k-meet-semidistributive. When k=1 they are known as meet-semidistributive lattices.We first give a polynomial time algorithm to compute an implicational base of a k-meet-semidistributive lattice from its associated colored poset. In other words, for a fixed k, finding a minimal implicational base of a k-meet-semidistributive lattice L from a context (FCA literature) of L can be done not just in output-polynomial time (which is open in the general case) but in polynomial time in the size of the input. This result generalizes that in [26]. Second, we derive an algorithm to compute a set-colored poset from an implicational base which is based on the enumeration of minimal transversals of a hypergraph and turns out to be in polynomial time for k-meet-semidistributive lattices [13,20]. Finally, we show that checking whether a given implicational base describes a k-meet-semidistributive lattice can be done in polynomial time

Eighth International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI at ECAI 2020)

International audienceProceedings of the 8th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2020)co-located with 24th European Conference on Artificial Intelligence (ECAI 2020), Santiago de Compostela, Spain, August 29, 202