State Consistency In Petri Nets Hierarchy Modeling

There will always be too many nodes when using the Petri net to model complex system. The increase of nodes will cause the combination of state number grows as the exponential function, which is the so-called state space problem. The reason is that objective world itself has a hierarchical structure but the Petri net not, so it cannot reduce the complexity of the system through hierarchical modeling.There are two ways to solve the state space explosion problem of the Petri net:adopt advanced Petri net modeling or the hierarchical modeling. However, when using the advanced Petri net to model complex system, the number of nodes will be reduced and at the same time the complexity of understanding the model will be increased. The main approach is to establish hierarchical structure of the Petri net, but the existing research work requires subnet for refining operation must have some certain structure, which leads to modeling ability of the Petri net been restricted to a certain extent. In addition, the importance of existing work is focus on constitutive property of hierarchical structure of the Petri net, while ignoring the most basic requirements of it, that is whether to keep state consistency before and after refining operation.This article from angle of refining transition of the Petri net, provides the WS-TT subnet which has complex structure and be used for refined operation, it also ensures state consistency of the Petri net. The main works are as follows:(1) In order to solve the state space explosion problem, we establish the Petri net which has hierarchical structure from the angle of refining transition. At the same time, we discuss the most basic property in hierarchical structure of the Petri net, and provide the definition of state consistency as well as the detection algorithm.(2) In order to maintain the state consistency of hierarchical structure of the Petri, we present the WS-TT subnet of good structure, which is used for refining transition, and we also prove this type of subnet meets state consistency during refining transition process. At the same time, we provide an algorithm in order to determine whether the subnet is WS-TT subnet.(3) In the application and implementation, we apply operation of refining transition of the WS-TT subnet to the field of software evolution modeling, which makes up for the lack of modeling capability resulted by basic refining transition. In addition, we implement the algorithm of determining the WS-TT subnet through open source tool PIPE to provide strong support for the verification of state consistency of the Petri net modeling.