Roots and Powers of Regular Languages

@inproceedings{Horvth2002RootsAP,
  title={Roots and Powers of Regular Languages},
  author={S{\'a}ndor Horv{\'a}th and Peter Leupold and Gerhard Lischke},
  booktitle={Developments in Language Theory},
  year={2002}
}
For a set H of natural numbers, the H-power of a language L is the set of all words p where p ∈ L and k ∈ H. The root of L is the set of all primitive words p such that p belongs to L for some n ≥ 1. There is a strong connection between the root and the powers of a regular language L namely, the H-power of L for an arbitrary finite set H with 0, 1, 2 / ∈ H is regular if and only if the root of L is finite. If the root is infinite then the H-power for most regular sets H is context-sensitive but… CONTINUE READING