| Project/Area Number |
25330020
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | National Institute of Informatics |
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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)
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| Research Collaborator |
SALVATI Sylvain INRIA Bordeaux
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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