Asymptotic Approximation by Regular Languages

This paper investigates a new property of formal languages called \(\mathrm {REG}\)-measurability where {REG}\) is the class regular languages. Intuitively, language \(L\) {REG}\)-measurable if there exists an infinite sequence that “converges” to \(L\). A without has complex shape in some sense so it can not be (asymptotically) approximated by We show several context-free are (including with transcendental generating function and density, particular), while certain simple deterministic set primitive words {REG}\)-immeasurable strong sense.