Structural Simplification of Finite State Machines using Pruning Operators based on Semi-Tensor Product of Matrices

In this paper, we consider the problem of structural simplification of finite state machines (FSMs), aiming at designing a structural simplification filter for FSMs by constructing pruning operators within the framework of the semi-tensor product of matrices (STP), where the FSM is considered as a logical dynamical system. The concept of pruning operators is proposed by incorporating the physical meaning of FSM state transitions into its dynamic equations. Therefore, to simplify the FSM state space, we construct pruning operators for eliminating redundant states and their additional transitions, respectively. In addition, we further design the corresponding algorithms based on these mathematical descriptions to make the physical meaning of FSM state-space optimization clearer. The validity and correctness of the conclusions are verified using the corresponding language models. The proposed pruning operators lay the foundation for performing state-space optimization and may have a wide range of application scenarios.