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DOI: 10.4230/LIPIcs.ICALP.2017.97
URN: urn:nbn:de:0030-drops-74323
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7432/
Asada, Kazuyuki ; Kobayashi, Naoki
Pumping Lemma for Higher-order Languages
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Abstract
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.
BibTeX - Entry
@InProceedings{asada_et_al:LIPIcs:2017:7432,
author = {Kazuyuki Asada and Naoki Kobayashi},
title = {{Pumping Lemma for Higher-order Languages}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {97:1--97:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-041-5},
ISSN = {1868-8969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7432},
URN = {urn:nbn:de:0030-drops-74323},
doi = {10.4230/LIPIcs.ICALP.2017.97},
annote = {Keywords: pumping lemma, higher-order grammars, Kruskal's tree theorem}
}
| Keywords: | pumping lemma, higher-order grammars, Kruskal's tree theorem | |
| Seminar: | 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 07.07.2017 |
