Nested Petri nets and loaded inscription labels: distributed system and recursion

For modeling concurrent processes, complex multi-level systems without additional places, transitions, and their relationships, synchronization of different flows of information and views on different nets of the same places with different markings, nested Petri nets are used. An alternative to this type of the nets are nets with loaded inscription labels containing additional information about the structure of the system or history of its changes. Comparison of the approaches to construction of Petri nets based on the nested nets and nets with loaded inscription labels is made by the example of the analysis of the distributed system of car rent agency and the recursive task — finding factorial. The analysis of the distributed system of the agency is made on the basis of two-level nested Petri nets using vertical and horizontal synchronization. In order to compare, the analysis based on the loaded inscriptional labels is carried out in two ways. In the first case, the structure of the system net is taken as a basis; in the second case the net consists of three parts, to each of which a certain set of data types is added to display the possible system states. Finding factorial of the number $y$ in the nested Petri nets is made through vertical synchronization of transitions between the system net and the element nets, and while using the loaded inscription labels it is carried out via the combined data type of the net parts. The variable of the first data type displays the number of the desired factorial, and in the second case the value of the current variable calculated in the previous step is observed. Modeling and automatic analysis of Petri nets for these examples occur in the software environment CPN Tools (version 4.0.0).