Caratheodory Extensions of Subclasses of Regular Languages

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 C of regular languages, we show that the class of all C-measurable regular languages has a good algebraic structure.