共享合成Petri网系统的语言递归性与系统活性

在Perri网系统合成操作的研究中,大系统的一些好性质,如活性、无死锁性的判定,是一个重要的研究内容.研究了Petri网系统的一种重要的合成操作--共享合成,着重研究了Petri网系统共享合成的行为关系(语言关系),指出并证明了Petri网系统共享合成过程中语言的递归性质,得到一个并发语言形式的共享合成语言关系式.这个语言关系式为应用Petri网系统对具有并发行为特征的系统进行建模分析提供了一种有效的形式化工具.进而利用这个语言关系式来判定共享合成网系统的活性与无死锁性，得到共享合成网系统活及无死锁的充要条件.最后给出了一些条件,在这些条件下,可用小系统的语言子集来判定共享合成网系统的活性,从而达到用小系统来研究大系统活性的目的.

Language Recursiveness and Liveness in Sharing Synthesis of Petri Net Systems

The determination of such good properties as liveness, deadlock-freeness of a global system is an important field in the study of Petri net systems synthesis. In this paper, the sharing synthesis of Petri net systems, a significant synthesis process, is discussed. The language recursiveness in sharing synthesis process is proposed and proved, and then the language relation formula based on the concurrent language is obtained. These results present a formal tool for the analysis of a large system which contains concurrent behavior. Moreover, this language relation formula can be applied to judge the liveness and deadlock-freeness of the synthesized systems. Necessary and sufficient conditions are developed. Finally, under the given conditions, the liveness of a global system can be determined by the sublanguage of the local systems, and thus can be studied by means of local systems.