On all things star-free
Formal Languages and Automata Theory
2019-04-29 v1
Abstract
We investigate the star-free closure, which associates to a class of languages its closure under Boolean operations and marked concatenation. We prove that the star-free closure of any finite class and of any class of groups languages with decidable separation (plus mild additional properties) has decidable separation. We actually show decidability of a stronger property, called covering. This generalizes many results on the subject in a unified framework. A key ingredient is that star-free closure coincides with another closure operator where Kleene stars are also allowed in restricted contexts.
Cite
@article{arxiv.1904.11863,
title = {On all things star-free},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1904.11863},
year = {2019}
}