## 2 Related Work
### Conflict Problems and Solutions in Petri Net  
In the manufacturing system, the process of decision-making, planning, scheduling, management or operation of a limited number of options is a knowledge-based decision tree (multi-tree). The result is to choose a feasible, correct or optimal branch to proceed, which is very consistent with the Petri net conflict selection problem, as manifested in Figure 2. Unfortunately, Petri net also has some theoretical problems to be solved. When there is more than one transition in the post-set of one place, the conflict of free choice occurs. Correspondingly, the conflict phenomenon is equivalent to the problems to be determined in the system, such as task scheduling, intelligent decisions, etc. Therefore, solving the knowledge-based decision problem in the actual production operation process of the factory is equivalent to solving the Petri net free-choice conflict phenomenon. Many scholars have studied the conflict of a Petri net. Starting with the influence of the directed loop of a Petri net on structural activity, the structural activity of a conflict-free Petri net was analyzed and determined in [32]. Further, the relevant conditions and conclusions of the methods for determining the structural activity of this kind of Petri net were studied, and it was concluded that a conflict-free Petri net is a necessary and sufficient condition to satisfy the structural activity. In the case of conflict, the choice of which transition is enabled is completely uncertain, and the enablement of either transition is possible. At the same time, the enablement of one transition makes other transitions impossible. In the timed Petri net model, there are several kinds of simple strategies that can be applied:  
1. The first is to set priorities and determine the priority of transition enablement. In this case, transitions with high priority can be enabled, while transitions with low priority cannot be enabled. For example, in the PIPE v4.3.0 version of the Petri net simulation tool, this method is applied to resolve conflicts. In addition, ref. [33] proposed a hybrid timed Petri net modeling method with test arcs to solve the problem of resource conflict between time and space in distributed systems. Additionally, it uses the priority function to determine the order of conflict transitions so as to achieve the purpose of resolving conflicts in the distributed shunting system of train stations. 2. The second method depends on the firing time of the transition. In this case, if the post-set consists of an immediate transition and a time transition, the immediate transition is enabled while the time transition is not enabled. Further, if all options are time transitions, the transition that has the shortest firing time is enabled. 3. The third method is to change the network structure, such as upgrading Petri nets to advanced net systems: predicate/transition systems or colored net systems [34]. In this case, transitions that satisfy the enabled condition's predicate or color requirements can be enabled. However, the existence of an advanced network increases the complexity of the network and makes readability worse. Figure 2: Decision tree and Petri net. The above strategies can better solve the conflict problem in an environment with strict order. With the deepening of research, there are many methods of conflict detection and resolution. Ref. [35] extended the UML activity graph and used the method of graph simplification to reduce the model to an appropriate scale, thus realizing a conflict detection algorithm. At the same time, by analyzing the causes of various conflicts, corresponding conflict resolution schemes were given. In [36], behavior modeling based on Petri net was introduced, and a multi-domain hierarchical mapping model of a complex technology system was constructed by using the decomposition mapping method of top-down and bottom-up. Afterwards, conflicts were located with the help of Petri-net-related tools and were resolved by applying TRIZ.