This chapter is dedicated to several structure features of Petri nets. There is detailed description of appropriate access in Petri nets and reachable tree mechanism construction. There is an algorithm that describes the minimum sequence of possible transitions. The algorithm developed by us finds the shortest possible sequence for the network promotion state, which transfers the mentioned network state to the coverage state. The corresponding theorem is proven, which states that due to the describing algorithm, the number of transitions in the covering state is minimal. This chapter studies the interrelation of languages of colored Petri nets and traditional formal languages. The Venn diagram, modified by the author, is presented, which shows the relationship between the languages of the colored Petri nets and some traditional languages. As a result, it is shown that the language class of colored Petri nets includes an entire class of context-free languages and some other classes. The results obtained show that it is not possible to model the Patil problem using the well-known semaphores P and V or classical Petri nets, so the mentioned systems have limited properties.
Part of the book: Numerical Modeling and Computer Simulation