Complexity Results for Implication Bases of Convex Geometries
Computational Complexity
2022-11-17 v1
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.
Cite
@article{arxiv.2211.08524,
title = {Complexity Results for Implication Bases of Convex Geometries},
author = {Todd Bichoupan},
journal= {arXiv preprint arXiv:2211.08524},
year = {2022}
}