An empirical study on the complexity metrics of Petri nets

Abstract

In this paper, we study the complexity metrics of Petri nets. We define some structural complexity metrics, such as volume and cyclomatic number, and dynamic complexity metrics, such as number of node and degree of parallelism in the reachability tree. By empirical study of 75 randomly selected practical Petri nets, we obtain correlation coefficients among 15 defined metrics and find some interesting results. Adapting the maximum firing rule and maximal reduced Petri net, we can reduce the complexity, even though we lose some state information. However, the maximum firing rule, like the clique problem, is an NP-hard problem. Modeling a maximum concurrency scheduling in concurrent systems by Petri nets, we can make use of the results for predicting the amount of effort required in modeling and analysis.