Adaricheva, Kira2016-02-092016-02-092016Adaricheva Kira; 2016; Optimum basis of finite convex geometry; arXiv.orghttp://nur.nu.edu.kz/handle/123456789/1210Convex geometries form a subclass of closure systems with unique criticals, or UC-systems. We show that the F-basis introduced in [6] for UC- systems, becomes optimum in convex geometries, in two essential parts of the basis: right sides (conclusions) of binary implications and left sides (premises) of non-binary ones. The right sides of non-binary implications can also be optimized, when the convex geometry either satis es the Carousel property, or does not have D-cycles. The latter generalizes a result of P.L. Hammer and A. Kogan for acyclic Horn Boolean functions. Convex geometries of order convex subsets in a poset also have tractable optimum basis. The problem of tractability of optimum basis in convex geometries in general remains to be openenAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICSfinite convex geometryArticle