Regular tree languages in low levels of the Wadge Hierarchy
Miko{\l}aj Boja\'nczyk, Filippo Cavallari, Thomas Place, Micha{\l}, Skrzypczak

TL;DR
This paper characterizes regular infinite tree languages within low Wadge hierarchy levels, providing decidability results for specific classes including Boolean combinations of open sets and the Borel class Delta2.
Contribution
It offers effective characterizations and decidability results for regular tree languages in low Wadge hierarchy levels, including finite levels, BC(Sigma_1^0), and Delta_2^0.
Findings
Decidability for finite levels of the hierarchy
Decidability for BC(Sigma_1^0) class
Decidability for Delta_2^0 Borel class
Abstract
In this article we provide effective characterisations of regular languages of infinite trees that belong to the low levels of the Wadge hierarchy. More precisely we prove decidability for each of the finite levels of the hierarchy; for the class of the Boolean combinations of open sets (i.e. the union of the first levels); and for the Borel class (i.e. for the union of the first levels).
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