On the automata functional systems

The paper gives the main results on the problems of expressibility and completeness for the automata functional systems. These results were obtained in the more than 30 past years, that is, since the appearance and during the years of formation of automata theory. The description of the properties of the automata functional systems is done for model systems in order of increasing their complexity. The first to be considered are automata without memory, i.e., the functions of $k$-valued logic, then we consider automata with limited memory, i.e., the above-mentioned functions with delays, and finally, finite automata, i.e., automata functions.