Calculation and Analysis of Petri Net Reachability Graphs by a Think-Globally-Act-Locally Method

A think-globally-act-locally (TGAL) technique is proven to be an effective method to address the state explosion issue for complex discrete event systems modeled with Petri nets. This paper introduces a TGAL-based method for computing and analyzing the reachability graph (RG) of Petri net models. Given a net system, the TGAL technique strategically introduces a global idle place (GIP) to iteratively generate its RG by updating the token count. At each step, the reachable markings (RMs) and legal markings (LMs) obtained by the previous iterations are considered to calculate the corresponding states of the current step. According to the enforced control requirement, a system state is required to be computed and classified only once during an iterative process. This method only calculates the necessary number of RMs and reduces computational redundancy, which minimizes the computational cost. Four typical Petri net models from existing studies are employed to demonstrate the method.