Feedback connection in recurrent circuits

It is shown that, under some natural restrictions on the element basis, for any recurrent circuit with a fixed number of inputs, it is possible to construct a circuit functionally equivalent to it in the same basis using superposition operations and no more than a double application of the feedback operation with a linear increase in the number of delays used compared to original circuit implementation. Thus, the linearity of the order of memory growth in the transition to the optimal (in terms of the number of delays) scheme with no more than two feedbacks has been proved. Short-term and long-term memory modules are distinguished in the structure of the recurrent circuits with no more than two feedbacks constructed in the work. The result obtained, in particular, is valid for the class of finite automata, as well as for the class of neural circuits built from elements containing gates.