Size-preserving translations from order-(n + 1) word grammars to order-n tree grammars

Kazuyuki Asada, Naoki Kobayashi

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

Abstract

Higher-order grammars have recently been studied actively in the context of automated verification of higher-order programs. Asada and Kobayashi have previously shown that, for any order-(n + 1) word grammar, there exists an order-n grammar whose frontier language coincides with the language generated by the word grammar. Their translation, however, blows up the size of the grammar, which inhibited complexity-preserving reductions from decision problems on word grammars to those on tree grammars. In this paper, we present a new translation from order-(n + 1) word grammars to order-n tree grammars that is size-preserving in the sense that the size of the output tree grammar is polynomial in the size of an input tree grammar. The new translation and its correctness proof are arguably much simpler than the previous translation and proof.

Original languageEnglish
Title of host publication5th International Conference on Formal Structures for Computation and Deduction, FSCD 2020
EditorsZena M. Ariola
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771559
DOIs
Publication statusPublished - 2020 Jun 1
Event5th International Conference on Formal Structures for Computation and Deduction, FSCD 2020 - Virtual, Online, France
Duration: 2020 Jun 292020 Jul 6

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume167
ISSN (Print)1868-8969

Conference

Conference5th International Conference on Formal Structures for Computation and Deduction, FSCD 2020
CountryFrance
CityVirtual, Online
Period20/6/2920/7/6

Keywords

  • Complexity
  • Higher-order grammar
  • Tree language
  • Word language

ASJC Scopus subject areas

  • Software

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