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math.OC2012★ 2 cited
Optimum basis of finite convex geometry
Kira Adaricheva
Convex geometries form a subclass of closure systems with unique criticals, or -systems. We show that the -basis introduced in [1] for -systems, becomes optimum in conve…
math.OC2012★ 18 cited
On implicational bases of closure systems with unique critical sets
Kira Adaricheva, J. B. Nation
We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean…