Mathematical study of Constructive Concurrent and Distributed Programm system

构造性并发分布式程序系统的数学研究

• 批准号: 09640302
• 负责人: TAKAYAMA Yukihide
• 金额: $ 2.11万
• 依托单位: Ritsumeikan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640302/
• 关键词: constructive programming; concurrency theory; computer algebra

First of all, we developed a prototype of linear logic prover system, which is a subsystem of our Rits Concurrency Workbench - an experimental programming system based on pi calculus and Linear Logic. Also, we fixed a final version of the theory of concurrency analysis based on homotopy model of concurrent computation.For computer algebra, we improved efficiency of our set constraint solver system by refining algorithms in the program and developed a prototype GUI system for displaying the set constraint. Also, we found a drastically new method for parallelize the Boolean Gr6bner basis algorithm, which is the core part of the set constraing solver, and carried out implementation in two different programming languages, KLIC and Asir. Based on this idea, we triecl to find parallelized algorithm of Grobner basis for von neumann regular ring, which is an extension of Boolean Grobner basis.Finally, we obtained an interesting result relating both to concurrent programming and computer algebra. By using combinatorial commutative ring theory and algebraic topology, we founci an effective method for checking Cohen-Macaulayness of a simplicial complex by analysing the 1-skeleton of the complex. This result has close relation with partially ordered set, which is useful for modeling structure of concurrent computation.

首先，我们开发了一个线性逻辑证明器原型系统，它是我们的Rits并发实验系统的一个子系统-一个基于π演算和线性逻辑的实验编程系统。同时，基于并发计算同伦模型，对并发分析理论进行了修正;针对计算机代数问题，改进了集合约束求解系统的算法，提高了求解效率，并开发了一个集合约束显示的GUI原型系统。同时，我们还对集合约束求解器的核心部分布尔Gr 6 bner基算法提出了一种全新的并行化方法，并用KLIC和Asir两种不同的编程语言进行了实现。基于这一思想，我们尝试寻找von Schann正则环的Grobner基的并行算法，它是布尔Grobner基的推广，最后得到了一个与并发程序设计和计算机代数有关的有趣结果。本文利用组合交换环理论和代数拓扑学，通过对单纯复形的1-骨架的分析，找到了一个检验其Cohen-Macaulay性的有效方法。这一结果与偏序集有着密切的联系，对并行计算的结构建模有一定的指导意义。

项目成果

高山幸秀: "Towards cycle filling as parallelization" 数理解析研究所講究録996. 207-221 (1997)

Yukihide Takayama：“以并行化方式实现循环填充” 数学研究所 Kokyuroku 996. 207-221 (1997)

K.Doi, H.Hida and H.Ishii: "Discriminant of Hecke fields and the twisted adjoint L-values for GL(2)" Inventiones Mathematicae. (in print). (1999)

K.Doi、H.Hida 和 H.Ishii：“Hecke 域的判别式和 GL(2) 的扭曲伴随 L 值”数学发明。

高山幸秀, 日比孝之: "Steinitz' theorem ahologue for two dimensional Cohen-Macaulay complexes" Advances in Applied Mathematrcs. 22. 200-218 (1999)

Yukihide Takayama、Takayuki Hibi：“二维 Cohen-Macaulay 复合体的 Steinitz 定理同源物”应用数学进展 22. 200-218 (1999)。

佐藤洋祐: "Sefcoustraint Solver-Grobner basis for non-numericol domains" Proceedings of International Symposium on Symbolic and Algebraic Computation. 13-14 (1997)

Yosuke Sato：“非数值域的 Sefcoustraint Solver-Grobner 基础”国际符号和代数计算研讨会论文集 13-14 (1997)。

土井公二, 肥田晴三, 石井秀則: "Discriminant of Hecke fields and the twisted adjoint L-values for GL(2)" Invensiones Mathematicae. 印刷中. (1999)

Koji Doi、Harumi Hida、Hidenori Ishii：“Hecke 域的判别式和 GL(2) 的扭曲伴随 L 值”Inventiones Mathematicae (1999)。