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URN: urn:nbn:de:0030-drops-62469
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On Word and Frontier Languages of Unsafe Higher-Order Grammars

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Abstract

Higher-order grammars are an extension of regular and context-free grammars, where nonterminals may take parameters. They have been extensively studied in 1980's, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result.

BibTeX - Entry

@InProceedings{asada_et_al:LIPIcs:2016:6246,
  author =	{Kazuyuki Asada and Naoki Kobayashi},
  title =	{{On Word and Frontier Languages of Unsafe Higher-Order Grammars}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{111:1--111:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6246},
  URN =		{urn:nbn:de:0030-drops-62469},
  doi =		{10.4230/LIPIcs.ICALP.2016.111},
  annote =	{Keywords: intersection types, higher-order grammars}
}

Keywords: intersection types, higher-order grammars
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue date: 2016
Date of publication: 2016


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