Descriptive Set Theory and $\omega$-Powers of Finitary Languages

Olivier Finkel; Dominique Lecomte

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arXiv · 2007.08636

Descriptive Set Theory and $\omega$-Powers of Finitary Languages

Olivier Finkel·Dominique Lecomte

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Abstract

The $\omega$-power of a finitary language L over a finite alphabet $\Sigma$ is the language of infinite words over $\Sigma$ defined by L $\infty$ := {w 0 w 1. .. $\in$ $\Sigma$ $\omega$ | $\forall$i $\in$ $\omega$ w i $\in$ L}. The $\omega$-powers appear very naturally in Theoretical Computer Science in the characterization of several classes of languages of infinite words accepted by various kinds of automata, like B{\"u}chi automata or B{\"u}chi pushdown automata. We survey some recent results about the links relating Descriptive Set Theory and $\omega$-powers.

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Olivier Finkel, Dominique Lecomte. 2020-07-15. Descriptive Set Theory and $\omega$-Powers of Finitary Languages. https://arxiv.org/abs/2007.08636

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