Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 [1] 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.
  [1] K. Adaricheva and J.B.Nation, On implicational bases of closure systems
with unique critical sets, arxiv:1205.2881

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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: funct-an