@InProceedings{carayol_et_al:LIPIcs.ICALP.2024.131, author = {Carayol, Arnaud and Charamond, Lucien}, title = {{The Structure of Trees in the Pushdown Hierarchy}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {131:1--131:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.131}, URN = {urn:nbn:de:0030-drops-202749}, doi = {10.4230/LIPIcs.ICALP.2024.131}, annote = {Keywords: Pushdown hierarchy, Monadic second-order logic, Automatic numbers} }