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

2015 Fiscal Year Final Research Report

• 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
• 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.

Free Research Field

数理言語学