Complexity Results for Implication Bases of Convex Geometries

Todd Bichoupan

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arXiv · 2211.08524

Complexity Results for Implication Bases of Convex Geometries

Todd Bichoupan

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Abstract

A convex geometry is finite zero-closed closure system that satisfies the anti-exchange property. Complexity results are given for two open problems related to representations of convex geometries using implication bases. In particular, the problem of optimizing an implication basis for a convex geometry is shown to be NP-hard by establishing a reduction from the minimum cardinality generator problem for general closure systems. Furthermore, even the problem of deciding whether an implication basis defines a convex geometry is shown to be co-NP-complete by a reduction from the Boolean tautology problem.

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Todd Bichoupan. 2022-11-15. Complexity Results for Implication Bases of Convex Geometries. https://arxiv.org/abs/2211.08524

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