Thicket Density
Logic
2023-06-22 v4
Abstract
We define a new type of "shatter function" for set systems that satisfies a Sauer-Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah's 2-rank instead of VC dimension. We identify the rate of growth of this shatter function, the quantity analogous to VC density, with Shelah's -rank.
Cite
@article{arxiv.1702.03956,
title = {Thicket Density},
author = {Siddharth Bhaskar},
journal= {arXiv preprint arXiv:1702.03956},
year = {2023}
}
Comments
15 pages, 7 figures