SYSTEMATIC ANALYSIS AND DESIGN OF LARGE SCALE CONCURRENT SYSTEMS BY USING QUANTUM NET MODEL

为了系统地分析和设计由网络连接的大型并发系统，我们进行了理论研究，并开发了如下的CAD程序。研究：利用Petri网的可达性可以解决系统控制问题，利用Petri网的活动性可以解决系统死锁问题。因此，首先，为了处理网络和大规模并发系统中的模糊信息，我们引入了以复数为参数的新型扩展Petri网。其次，为了证明这种扩展Petri网（量子Petri网）的实用性，我们推导了更多有用的条件来检查其在子类中的结构性质和行为性质。特别是，这些条件可以很容易地检查，因为它们以初始令牌分布、最终令牌分布和网络结构的方式呈现。CAD程序的开发：我们准备利用上述理论成果及其程序包（有界性、可达性、活动性等）对大规模并发系统进行系统的分析和设计。结果：这些结果出现在以下论文（11）中。引用)。

In order to analyze and design systematically the large scale concurrent systems connected by networks, we investigate theoretically and develop the CAD programs as follows.Investigation:The problem of system control can be solved by using reachability of Petri nets and the problem of system deadlock can be solved by using liveness of Petri nets.Therefore, first, in order to deal with the fuzzy information in the networks and the large scale concurrent systems, we introduced new extended Petri nets which can use the complex number as parameters.Next, in order to show the usefulness of this extended Petri net (Quantum Petri net), we derived more useful condition for checking its structural properties and behavioral properties in subclasses. In particular, these conditions can be checked easily because they are presented in terms of the initial token distribution, the final token distribution, and the net structure.Development of CAD Programs:We prepared to analyze and design systematically the large scale concurrent systems by using the above theoretical results and its program packages (boundedness, reachability, liveness, etc.).Results:These results are appeared in the following papers (11. REFERENCES).