2026-10-01T10:23:28Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7432 2026-09-23T00:50:25Z ddc:004 open_access

Pumping Lemma for Higher-order Languages Asada, Kazuyuki Kobayashi, Naoki pumping lemma higher-order grammars Kruskal's tree theorem We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kazuyuki Asada and Naoki Kobayashi 2017 Is Part Of LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2017.97 urn:nbn:de:0030-drops-74323 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.97 eng https://creativecommons.org/licenses/by/3.0/legalcode