Simplification of Extended Finite State Machines: A Matrix-Based Approach

Extended Finite State Machines play a crucial role in capturing complex behaviors and interactions in the field of system modeling and analysis. However, as the complexity of systems increases, so does the size and complexity of extended finite state machines. This poses challenges in terms of understanding, analyzing, and computing efficiency. Simplification is an effective method for complex systems in the field of system modeling and analysis. In this paper, we investigate the simplification problem of extended finite state machines using the semi-tensor product of matrices. Firstly, based on the semi-tensor product of matrices, we dynamically model the state transitions of extended finite state machines, successfully bridging the gap between extended finite state machines and control theory. Secondly, utilizing the state transition model of extended finite state machines, we introduce the concept of supervisors and provide a definition for supervisors. We propose a simplification algorithm that effectively reduces the complexity level of extended finite state machine systems. Finally, through examples demonstration we validate our conclusions’ correctness as well as demonstrate effectiveness our proposed algorithm.