Algebraic Implementation of Extended Finite State Machine Networks

The traditional implementation method for finite state machine networks fails to explicitly define the mathematical relationship between the dynamics of the entire network and the dynamics of individual components. This paper investigates the implementation of extended finite state machine networks from an algebraic perspective, aiming to establish a mathematical expression between the dynamics of whole network and dynamics of the components. Two common types of extended finite state machine networks are considered: product networks of extended finite state machines and parallel networks of extended finite state machines. The algebraic implementation methods for both types are established. The implementation technique involves performing "algebraic composition of product" on the dynamic matrices of component finite state machines within the STP framework. The composed dynamic matrix fully characterizes the dynamic behavior of the product network of extended finite state machines and explicitly defines the relationship between the dynamics of the entire network and those of individual components. Subsequently, modify the parallel network of extended finite state machines and then use the algebraic composition established for the product network to realize the algebraic implementation of the parallel network of extended finite state machines.