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.2016.111
URN: urn:nbn:de:0030-drops-62469
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Asada, Kazuyuki ; Kobayashi, Naoki

On Word and Frontier Languages of Unsafe Higher-Order Grammars

LIPIcs-ICALP-2016-111.pdf (0.6 MB)


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

  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 and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  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
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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