License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.97
URN: urn:nbn:de:0030-drops-74323
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7432/
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Asada, Kazuyuki ; Kobayashi, Naoki

Pumping Lemma for Higher-order Languages

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LIPIcs-ICALP-2017-97.pdf (0.6 MB)

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
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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