A Numerical Aggregation Method for Finite-State Machines Using Algebraic Operations

Abstract. This paper considers the problem of synthesizing finite-state machines (FSMs) based on algebraic methods. The aggregation operations of FSMs are numerically implemented using symbolic matrices that describe their functioning. An algebra is defined for these matrices as follows: the carriers are matrix elements and special symbols, and the signature includes two operations serving to determine actions over these symbols. As a result, it becomes possible to define an algebra of symbolic matrices whose signature includes three operations. The classical operations over FSMs are represented in matrix form based on the algebra of symbolic matrices. Next, special operations over FSMs are constructed involving classical operations over them. Special operations are constructed considering the constraints and requirements of the subject area. A numerical example of FSM synthesis––the joint activity of two functional groups in an emergency zone––is provided.

Keywords: synthesis of automata, algebra of automata, symbolic matrices.