2015 Fiscal Year Final Research Report
A Study of Tree and String Languages Generated by Context-Free Tree Grammars
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 |
Section | 一般 |
Research Field |
Theory of informatics
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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)
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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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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 |
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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Free Research Field |
数理言語学
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