A funtadamental study on graph transforamtion systems with relational calculus

基于关系演算的图变换系统的基础研究

• 批准号: 07680363
• 负责人: KAWAHARA Yasuo
• 金额: $ 1.47万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07680363/
• 关键词: graph transformation; graph grammar; relational calculus; relation algebra; category theory; fuzzy set; fuzzy relation; fuzzy graph; 関係代数; ファジィ集合; ファジィ関係; ファジィグラフ

This reseach project obtained the following results :・We developed an axiomatic formalisation of fuzzy relation algebras as a foundation of fuzzy relational calculus. By using the formalisation we generalized the representation problem for relation algebras, due to A.Tarski, to a representation problem for Dedekind and Zadeh categories, and we gave proofs of the representation problem for Dedekind and Zadeh categories.・We proposed a new matching method for fuzzy graphs in a theory of fuzzy graph transformations based on fuzzy relational calculus. Then we proved the existence of pullbacks in a category of fuzzy graphs, which gurantees the foundation for pullback graph transformations.・We invented relational set theory as an important foundation for graph transformations as well as mathematics and theoretical computer science. Also, we investigated its applications from a quite wide view.・The detailed summary of this reseach project is described in the report of the reseach project (booklet), printed in Department of Informatics, Kyushu University. The head investigator, on behalf of investigators of the project, is grateful for giving the financial suport.

本研究取得了以下成果：·我们发展了模糊关系代数的公理形式化，作为模糊关系演算的基础。利用这种形式，我们将A.Tarski提出的关系代数的表示问题推广到Dedekind和Zadeh范畴的表示问题，并给出了Dedekind和Zadeh范畴的表示问题的证明。·在基于模糊关系演算的模糊图变换理论中，我们提出了一种新的模糊图匹配方法。然后证明了一类模糊图的拉回的存在性，为拉回图的变换奠定了基础。·我们发明了关系集合论，作为图形转换以及数学和理论计算机科学的重要基础。此外，我们还从相当广泛的角度研究了它的应用。·该研究项目的详细摘要载于该研究项目报告(小册子)，由九州大学信息学系印制。首席调查员代表该项目的调查员对给予该项目的财政支持表示感谢。

项目成果

Y.Kawahara: "Relational graph rewritings" Theoretical Computer Science. 141. 311-328 (1995)

Y.Kawahara：“关系图重写”理论计算机科学。

S.Inokuchi, T.Sato, A.hara, S.Kumamoto, H.-Y.Lee and Y.Kawahara: "Computational analysis of cellular automata with triplet transition rule." Research Report on Information Science and Electical Engineering of Kyushu University. 1(1). 79-84 (1996)

S.Inokuchi、T.Sato、A.hara、S.Kumamoto、H.-Y.Lee 和 Y.Kawahara：“具有三重态转移规则的元胞自动机的计算分析。”

S.Inokuchi: "Computational analysis of cellular automata with triplet transition rule" Research Report on Info.Sci.and Elect.Eng.of Kyushu University. 28. 79-84 (1996)

S.Inokuchi：“具有三重态转移规则的元胞自动机的计算分析”九州大学Info.Sci.and Elect.Eng.的研究报告。

Y.Kawahara: "Period lengths of cellular automata cam-90 with memory" Journal of Mathematical Physics. 38. 255-266 (1997)

Y.Kawahara：“带记忆的元胞自动机 cam-90 的周期长度”《数学物理杂志》。

Y.Kawahara: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

Y.Kawahara：“模糊关系的代数形式化”发表在《国际模糊集与系统杂志》上。