VC-dimension of short Presburger formulas
Danny Nguyen, Igor Pak
TL;DR
This paper investigates the VC-dimension of concise Presburger formulas, providing bounds that are nearly tight, which advances understanding of their complexity in computational geometry and logic.
Contribution
It establishes tight bounds on the VC-dimension of short Presburger formulas, a previously unexplored aspect of their complexity.
Findings
Derived lower bounds for VC-dimension.
Established upper bounds close to the lower bounds.
Bounds are tight up to a polynomial factor.
Abstract
We study VC-dimension of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the formula.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Rings, Modules, and Algebras · Advanced Algebra and Logic