Modular Reversibility Analysis in Self-loops Connections of Petri Net Systems

It is well known that the use of a modular approach for modeling has many advantages: it allows the modeler to consider different parts of the model independently of one another. A modular approach to analysis is also attractive: it often dramatically decreases the complexity of the analysis task. To create Petri net models of large systems, four bottom-up techniques, consisting of sharing operation, synchronous operation, self-loops connection as well as inhibitor-arc connection, have been developed. This paper focus on the concurrent behavior relation in self-loops connections of Petri net systems. First, for the property of dynamic invariance we show that it is possible to decide dynamic invariance of the global system from invariance of the individual modules. Second, for reversibility property we show that it is possible to construct reversibility of total modular system from reversibility of the individual modules without unfolding to the entire state space. Finally, we present some examples to illustrate the effectiveness of our approaches. The advantages of our approaches are in the context of concurrent language and can synthesize Petri net systems beyond asymmetric choice nets.