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A survey on difference hierarchies of regular languages

Olivier Carton ; Dominique Perrin ; Jean-Éric Pin.

Difference hierarchies were originally introduced by Hausdorff and they play an important role in descriptive set theory. In this survey paper, we study difference hierarchies of regular languages. The first sections describe standard techniques on difference hierarchies, mostly due to Hausdorff. We&nbsp;[&hellip;]

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Polishness of some topologies related to word or tree automata

Olivier Finkel ; Olivier Carton ; Dominique Lecomte.

We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.

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