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arXiv · 1904.11863

On all things star-free

Thomas Place·Marc Zeitoun
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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.

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Thomas Place, Marc Zeitoun. 2019-04-26. On all things star-free. https://arxiv.org/abs/1904.11863

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