一句话：给出正则无限树语言在 Wadge 层级低层的有效刻画，并证明相应成员性可判定。
论文研究无限树上的正则语言在 Wadge 层级中的位置问题。作者对 Wadge 层级的低层给出有效刻画，从而判定给定正则无限树语言是否属于这些层级。具体证明：每个有限层级、开集的布尔组合类 BC(Σ₁⁰)（前 ω 个层级的并），以及 Borel 类 Δ₂⁰（前 ω₁ 个层级的并），其成员性问题均可判定。该工作将正则树语言与描述集合论及自动机理论中的 Wadge 层级联系起来，为无限树语言在这些低层上的可判定性提供了理论结果。
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 $BC(\Sigma_1^0)$ (i.e. the union of the first $\omega$ levels); and for the Borel class $\Delta_2^0$ (i.e. for the union of the first $\omega_1$ levels).
@article{paperbot758,
title = {Regular tree languages in low levels of the Wadge Hierarchy},
author = {Mikołaj Bojańczyk and Filippo Cavallari and Thomas Place and Michał Skrzypczak},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 3},
year = {2019},
doi = {10.23638/lmcs-15(3:27)2019}
}