On word and frontier languages of unsafe higher-order grammars

Kazuyuki Asada, Naoki Kobayashi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

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.

Original languageEnglish
Title of host publication43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
EditorsYuval Rabani, Ioannis Chatzigiannakis, Davide Sangiorgi, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770132
DOIs
Publication statusPublished - 2016 Aug 1
Event43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy
Duration: 2016 Jul 122016 Jul 15

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume55
ISSN (Print)1868-8969

Conference

Conference43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
CountryItaly
CityRome
Period16/7/1216/7/15

Keywords

  • Higher-order grammars
  • Intersection types

ASJC Scopus subject areas

  • Software

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  • Cite this

    Asada, K., & Kobayashi, N. (2016). On word and frontier languages of unsafe higher-order grammars. In Y. Rabani, I. Chatzigiannakis, D. Sangiorgi, & M. Mitzenmacher (Eds.), 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 [111] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 55). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2016.111