有效模-n S-不变量与不可达性判定

Hohn F E提出用S-不变量判定Petri网不可达性的一个方法。Desel J指出，存在某些标识，用S-不变量无法判定其不可达性，但利用模-n S-不变量却可加以判定。然而，对于一个给定的标识，是否存在模-n S-不变量能判定该标识的不可达性。如果存在的话，又该如何求取这些模-n S-不变量，Desel J并未就这两个问题给出答案。该文提出了有效模-n S-不变量的概念，将上述问题转化为有效模-n S-不变量的存在性问题，并借助矩阵的整数分解给出了寻找有效模-n S-不变量的方法，有效解决了利用模-n S-不变量进行不可达性判定的问题。

Effective Modular-n S-invariant and Non-reachability Decidability

A method to decide the non-reachability of a marking using S-invariants is provided by Hohn F E; In fact, there exists some markings, the non-decidability of which can not be decided with S-invariants. But it can be decided with modular-n S-invariants. Desel J points it out in reference two. However, whether or not there exists some modular-n S-invariant, which can be used to decide the non-reachability property of a marking? And if such modular-n S-invariant exists, how to find it? There is no answer to both of the questions. The definition of effective modular-n S-invarients is given, and both of the problems can be solved with effective modular-n S-invarients. Furthermore, a method to find the effective modular-n S-invarients using the matrix integral decomposition is presented.