Submission date: 10 September 2021

Abstract:

We prove that, for any d linearly independent functions from some set into a d-dimensional vector space over any field, the family of zero sets of all non-trivial linear combination of these functions has VC-dimension and Littlestone dimension d-1. Additionally, we characterize when such families are maximal of VC-dimension d-1 and give a sufficient condition for when they are maximal of Littlestone dimension d-1.

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Full text arXiv 2109.04805: pdf, ps.