## Bojańczyk, Mikołaj and Cavallari, Filippo and Place, Thomas and Skrzypczak, Michał - Regular tree languages in low levels of the Wadge Hierarchy

lmcs:4647 - Logical Methods in Computer Science, September 4, 2019, Volume 15, Issue 3
Regular tree languages in low levels of the Wadge Hierarchy

Authors: Bojańczyk, Mikołaj and Cavallari, Filippo and Place, Thomas and Skrzypczak, Michał

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).

DOI : 10.23638/LMCS-15(3:27)2019
Volume: Volume 15, Issue 3
Published on: September 4, 2019
Submitted on: June 26, 2018
Keywords: Computer Science - Formal Languages and Automata Theory