Mathematical study of Constructive Concurrent and Distributed Programm system

首先，我们开发了一个线性逻辑证明系统的原型，它是我们的Rits并发工作台的一个子系统——一个基于圆周率演算和线性逻辑的实验编程系统。同时，我们确定了基于并发计算同伦模型的并发分析理论的最终版本。对于计算机代数，我们通过改进程序中的算法来提高集合约束求解系统的效率，并开发了一个用于显示集合约束的原型GUI系统。此外，我们发现了一种全新的方法来并行化布尔Gr6bner基算法，这是集合约束求解器的核心部分，并在KLIC和Asir两种不同的编程语言中进行了实现。基于这一思想，我们找到了von neumann正则环的Grobner基的并行化算法，该算法是对Boolean Grobner基的扩展。最后，我们得到了一个关于并发编程和计算机代数的有趣结果。利用组合交换环理论和代数拓扑，通过分析简单复形的1骨架，建立了一种检验简单复形的Cohen-Macaulayness的有效方法。该结果与部分有序集有密切的关系，对并行计算结构的建模有一定的指导意义。

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.