A Study of Tree and String Languages Generated by Context-Free Tree Grammars

• Project/Area Number: 25330020
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: National Institute of Informatics
• Principal Investigator: Kanazawa Makoto 国立情報学研究所, 情報学プリンシプル研究系, 准教授 (20261886)
• Research Collaborator: SALVATI Sylvain INRIA Bordeaux
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 単純文脈自由木文法 / 樹状指標文法 / 多重文脈自由文法 / 多次元木 / 表現定理 / Ogdenの補題 / Dyck木言語 / Weirの制御言語 / 制御言語 / IO文脈自由木文法 / 並列多重文脈自由文法 / 属性文法 / Dyck言語 / 指標文法 / 線形指標文法

Outline of Final Research Achievements

I obtained a Chomsky-Schuetzenberger-style representation theorem for simple context-free tree grammars. This theorem uses a notion of Dyck tree language, in contrast to Dyck languages used by Chomsky and Schuetzenberger. As an application of this theorem, I conceived a new grammar formalism called "arboreal indexed grammars", which exactly correspond to simple context-free tree grammars. I also obtained a representation theorem for the string languages of simple context-free tree grammars, which is a natural generalization of Weir's representation theorem for string languages of tree-adjoining grammars.
Further, I showed that an Ogden-style iteration theorem does not hold for the string languages of simple context-free tree grammars, and gave a sufficient condition for a multiple context-free grammar to satisfy an Ogden-style iteration theorem. Every language in Weir's control language hierarchy can be generated by a multiple context-free grammar satisfying this condition.

Research Products

• [Int'l Joint Research] INRIA(フランス)
• [Journal Article] Ogden's lemma, multiple context-free grammars, and the control language hierarchy (2016)
  • Author(s): Makoto Kanazawa
  • Journal Title: Lecture Notes in Computer Science Volume: 9618 Pages: 371-383
  • DOI: 10.1007/978-3-319-30000-9_29
  • ISBN: 9783319299990, 9783319300009
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A Generalization of Linear Indexed Grammars Equivalent to Simple Context-Free Tree Grammars (2014)
  • Author(s): Makoto Kanazawa
  • Journal Title: Lecture Notes in Computer Science Volume: 8612 Pages: 86-103
  • DOI: 10.1007/978-3-662-44121-3_6
  • ISBN: 9783662441206, 9783662441213
  • Peer Reviewed
• [Journal Article] Multi-dimensional trees and a Chomsky-Schuetzenberger-Weir representation theorem for simple context-free tree grammars (2013)
  • Author(s): Makoto Kanazawa
  • Journal Title: NII Technical Report Volume: NII-2013-003E Pages: 1-60
• [Presentation] Ogden's lemma, multiple context-free grammars, and the control language hierarchy (2016)
  • Author(s): Makoto Kanazawa
  • Organizer: Language and Automata Theory and Applications
  • Place of Presentation: プラハ（チェコ共和国）
  • Year and Date: 2016-03-16
  • Int'l Joint Research
• [Presentation] A generalization of linear indexed grammars equivalent to simple context-free tree grammars (2014)
  • Author(s): Makoto Kanazawa
  • Organizer: FG 2014: 19th Conference on Formal Grammar
  • Place of Presentation: Tuebingen, Germany
• [Remarks] Makoto Kanazawa
  • URL: http://research.nii.ac.jp/~kanazawa/