Algebraic methods of the synthesis of models based on the graphical representation of finite state machines

The issues of modeling objects and systems based on the graphical representation of finite state machines using algebraic methods are considered. The problem of finite state machines synthesis based on the construction of the algebra of their graphoids is solved. With this aim existing operations on finite state machines are transferred to their graphoids. Subject to additional requirements, that may emerge during the analysis of the subject area new operations are introduced. This defines the algebra of finite state machines graphoids, which enables the synthesis of graphoids for finite state machines models using the algorithm proposed by the authors. Statements confirming the correctness of the algorithm are proven. A numerical example of the finite state machines model graphoid synthesis for the joint actions of functional groups in an emergency area.