Abstract
A language \(L\) is said to be regular measurable if there exists an infinite sequence of regular languages that “converges” to \(L\). In [13], the author showed that, while many complex context-free languages are regular measurable, the set of all primitive words and certain deterministic context-free languages are regular immeasurable. This paper investigates general properties of measurability, including closure properties, decidability and different characterisation. Further, for a suitable subclass \({\mathcal C}\) of regular languages, we show that the class of all \({\mathcal C}\)-measurable regular languages has a good algebraic structure.
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Notes
- 1.
Here \(p\) can be \(0\) and we call a singleton \(\{q\}\) arithmetic progression in this case.
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This work was supported by JSPS KAKENHI Grant Number JP19K14582.
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Sin’ya, R. (2021). Carathéodory Extensions of Subclasses of Regular Languages. In: Moreira, N., Reis, R. (eds) Developments in Language Theory. DLT 2021. Lecture Notes in Computer Science(), vol 12811. Springer, Cham. https://doi.org/10.1007/978-3-030-81508-0_29
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