Asymptotic Approximation by Regular Languages
Abstract
This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language is REG-measurable if there exists an infinite sequence of regular languages that "converges" to . A language without REG-measurability has a complex shape in some sense so that it can not be (asymptotically) approximated by regular languages. We show that several context-free languages are REG-measurable (including languages with transcendental generating function and transcendental density, in particular), while a certain simple deterministic context-free language and the set of primitive words are REG-immeasurable in a strong sense.
Keywords
Cite
@article{arxiv.2008.01413,
title = {Asymptotic Approximation by Regular Languages},
author = {Ryoma Sin'ya},
journal= {arXiv preprint arXiv:2008.01413},
year = {2020}
}
Comments
This is the full version of a paper accepted by SOFSEM 2021