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.FSTTCS.2018.14
URN: urn:nbn:de:0030-drops-99138
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9913/
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Asada, Kazuyuki ; Kobayashi, Naoki

Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered

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Abstract

Asada and Kobayashi [ICALP 2017] conjectured a higher-order version of Kruskal's tree theorem, and proved a pumping lemma for higher-order languages modulo the conjecture. The conjecture has been proved up to order-2, which implies that Asada and Kobayashi's pumping lemma holds for order-2 tree languages, but remains open for order-3 or higher. In this paper, we prove a variation of the conjecture for order-3. This is sufficient for proving that a variation of the pumping lemma holds for order-3 tree languages (equivalently, for order-4 word languages).

BibTeX - Entry

@InProceedings{asada_et_al:LIPIcs:2018:9913,
  author =	{Kazuyuki Asada and Naoki Kobayashi},
  title =	{{Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9913},
  URN =		{urn:nbn:de:0030-drops-99138},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.14},
  annote =	{Keywords: higher-order grammar, pumping lemma, Kruskal's tree theorem, well-quasi-ordering, simply-typed lambda calculus}
}

Keywords: higher-order grammar, pumping lemma, Kruskal's tree theorem, well-quasi-ordering, simply-typed lambda calculus
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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