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

中文翻译：

---

正则语言的渐近逼近

本文研究了形式语言的一种新属性，称为 REG 可测量性，其中 REG 是常规语言的类。直观地说，如果存在无限序列的常规语言“收敛”到 \(L\)，则语言 \(L\) 是 REG 可测量的。没有 REG 可测量性的语言在某种意义上具有复杂的形状，因此它不能（渐近地）被常规语言近似。我们证明了几种上下文无关语言是 REG 可测量的（尤其是具有先验生成函数和先验密度的语言），而某种简单的确定性上下文无关语言和原始词集在强烈意义上是 REG 不可测量的.