Algebra of Finite Automata as a Mathematical Model of the Digital Twin of Smart Production

The article is devoted to the development of the finite automata algebra of a special type DTA (Digital Twin Algebra), designed for mathematical modeling of production digital twins. The main attention is paid to the study of the composition operations of deterministic finite automata, which allow building models of composite assets from simpler ones. The DTA includes both well-known operations, for example, the operation of direct product of automata and the operation of superposition of automata, and newly introduced operations, including: operations of grouping finite automata into a parallel block, grouping of hierarchical structure, system composition, association between automata, recursive invocation of the automaton, asynchronous call of the automaton. The proposed mathematical apparatus can be used to develop formal models of behavior of production physical assets, their digital twins, as well as models of cyber-physical systems behavior, including both physical and virtual assets.