6 research outputs found
Optimum basis of finite convex geometry
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
ope
Optimum basis of finite convex geometry
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
ope