Abstract: The synchronic distance is not only an analyzing metric to describe the synchronic relationship between two events, but also a tool to represent the dynamic behavior of systems. However, it’s difficult to calculate the synchronic distance in a Petri net. The paper discusses the synchronic distance between any two subsets of transition in a P/T_net by using the principle of a weighted observe-place, and it points out that how to allocate a weight to an arc connecting a weighted observe-place and a transition by the definition of primitive weight function. In order to obtain the synchronic distance between two subsets of transition which are in the same fair-components, a synchronic observed P/T_system with weight is constructed. The maximum tokens and the minimum tokens in a weighted observe-place can be yielded during constructing the coverability tree of a original net system, therefore the synchronic distance between two subsets of transition is obtained, the corresponding algorithm is also given. The algorithm of computing the synchronic distance between any two subsets of transition in a P/T_system is given.

Key words: P/T_net, fair-components, weighted observe-place, synchronic observed P/T_system with weight, primitive weight function, synchronic distance

摘要： 同步距离既可以对两组事件之间同步程度进行定量分析，也可以刻画系统动态行为，然而Petri中同步距离计算一直存在难题。采用加权观察库所的原理讨论了P/T_网中任意两个变迁子集之间同步距离的计算，并通过本原权函数的定义指出了如何给连接变迁和加权观察库所之间的弧配置一个唯一的权值。为了得到处于同一个公平分支变迁子集之间的同步距离值，需构造一个带权同步观察P/T_系统，通过模拟原网系统的可覆盖树得到带权观察库所的最大和最小tokens，从而求得变迁子集之间的同步距离值，并给出相应算法，给出了求解P/T_网中任意两个变迁子集之间同步距离计算算法。

关键词: P/T_网, 公平分支, 带权观察库所, 带权同步观察P/T_系统, 本原权函数, 同步距离