eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-07-07
97:1
97:14
10.4230/LIPIcs.ICALP.2017.97
article
Pumping Lemma for Higher-order Languages
Asada, Kazuyuki
Kobayashi, Naoki
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol080-icalp2017/LIPIcs.ICALP.2017.97/LIPIcs.ICALP.2017.97.pdf
pumping lemma
higher-order grammars
Kruskal's tree theorem