Optimum basis of finite convex geometry
| dc.contributor.author | Adaricheva, Kira | |
| dc.date.accessioned | 2016-02-09T09:16:44Z | |
| dc.date.available | 2016-02-09T09:16:44Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Convex 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 open | ru_RU |
| dc.identifier.citation | Adaricheva Kira; 2016; Optimum basis of finite convex geometry; arXiv.org | ru_RU |
| dc.identifier.uri | http://nur.nu.edu.kz/handle/123456789/1210 | |
| dc.language.iso | en | ru_RU |
| dc.rights | Attribution-NonCommercial-ShareAlike 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/us/ | * |
| dc.subject | Research Subject Categories::MATHEMATICS | ru_RU |
| dc.subject | finite convex geometry | ru_RU |
| dc.title | Optimum basis of finite convex geometry | ru_RU |
| dc.type | Article | ru_RU |