Aspects of selection of SM Components with the application of the theory of hypergraphs

The paper discusses various aspects of selection of State Machine Components of a Petri net with the application of the theory of hypergraphs. First, the idea of selection of SM Components utilising the hypergraph apparatus is presented, then some examples of the exact transversal method, which has been successfully introduced as one of the alternative methods next to the exact algorithms (e.g. backtracking algorithm) that are commonly applied or approximate algorithms (e.g. greedy algorithm). The selection of subnets, which is essential for decomposition, is an NP-hard problem. In addition to the theoretical aspects, the article also presents the experimental research conducted in two phases. The first phase was designed to determine the effect of reduction, called Cyclic-Core, on the type of the selection hypergraph, on the basis of which the exact solution is later determined. The second part of the study deals with the efficiency and effectiveness of the exact transversal method, which provides a reference point, in comparison to the backtracking algorithm. The article has been complemented with a decent summary which includes: the issues discussed, the results of research, as well as references to the further stages of research.