English

Asymptotic Approximation by Regular Languages

Formal Languages and Automata Theory 2020-11-18 v2

Abstract

This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language LL is REG-measurable if there exists an infinite sequence of regular languages that "converges" to LL. 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

R2 v1 2026-06-23T17:37:37.155Z