Article ID Journal Published Year Pages File Type
4949515 Discrete Applied Mathematics 2017 10 Pages PDF
Abstract
Convex geometries form a subclass of closure systems with unique criticals, or UC-systems. We show that the F-basis introduced in Adaricheva and Nation (2014) 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 satisfies 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 open.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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