An interdisciplinary study on categorical computer mathematics

分类计算机数学的跨学科研究

• 批准号: 08304017
• 负责人: KAWAHARA Yasuo
• 金额: $ 6.08万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304017/
• 关键词: category theory; computer science; computational logic; relational calculus; artificial intelligence; programming semantics; computational complexity; constructive programming

This project was organized for investigations on categorical computer mathematics from inter-disciplinary viewpoints. All the investigators joining with this research project studied theoryﾟCof categories, Dedekind categories, final coalgebras, two-dimensional firing squad synchro-nization, proof and type theories, completeness for uniformly delayed circuits, symbolic and computational logics, inductive inference of real functions, intuitionistic and classical natural deduction systems with catch and throw rules, testing proofs by examples, and an approximation of protein threading, concerned with mathematics of category theory. As the results of the research projects we extensively developed computer mathematics in Japan, that is, we gave a lot of new theories of useful applied mathematics, proved new theorems in logic, category theory, automata theory, and artificial intelligence, and finally suggested new trends of contemporary applied mathematics.Also the head investigator organized the Japanese joint conferences of applied mathematics at Ryukoku University, Seta City in December 1996, December 1997 and December 1998. (This joint conference has rather long history about thirty years long.) The detailed summary of this research project is described in the report of the research project (booklet), printed in Department of Informatics, Kyushu University, March 1999. The head investigator, on behalf of investigators of the project, is grateful for giving the financial support.

该项目的组织目的是从跨学科的角度对分类计算机数学进行研究，所有参与该研究项目的研究人员都研究了Cof范畴、Dedekind范畴、最终余代数、二维射击队同步、证明和类型理论，均匀延迟电路的完整性、符号和计算逻辑、实函数的归纳推理、带有捕获和抛出规则的直观和经典的自然演绎系统、通过示例测试证明以及蛋白质的近似线程，涉及范畴论的数学，作为我们在日本发展计算机数学的研究项目的成果，也就是说，我们给出了很多有用的应用数学的新理论，证明了主要是逻辑、范畴论、自动机理论的新定理。并于1996年12月、1997年12月、1998年12月在濑田市龙谷大学组织了日本应用数学联合会议。会议的历史相当悠久，大约有三十年之久。）该研究项目的详细总结在九州大学信息学系1999年3月印刷的研究项目报告（小册子）中进行了描述。首席研究员代表该项目的研究人员感谢给予的财政支持。

项目成果

Kojiro Kobayashi: "On time optimal solutions of the two-dimensional firing squal synchronization problem" Proceedings of MFCS'98 Satellite Workshop on Cellular Automata. 17-26 (1998)

Kojiro Kobayashi：“二维发射方同步问题的时间最优解”MFCS98 元胞自动机卫星研讨会论文集。

Hiroakira Ono: "Decidability and the finite model property of substructural logics." CSLI Lecture Note. 263-274 (1997)

Hiroakira Ono：“可判定性和子结构逻辑的有限模型属性。”

Setsuo Arikawa: "Inductive inference of real functions." Theoretical Computer Science.(To appear).

Setsuo Arikawa：“实函数的归纳推理。”

T.Hikita: "Completeness for uniformly delayed circuits,a survey" To appear in Proc.of Conf.on Algebra and Combinatorics. (1997)

T.Hikita：“均匀延迟电路的完整性，一项调查”出现在 Proc.of Conf.on Algebra and Combinatorics 中。

Setsuo Arikawa: "Inductive inference of real functions" To appear in Theoretical Computer Science.

Setsuo Arikawa：“实函数的归纳推理”出现在《理论计算机科学》中。