Use of Unilateral Rings to Simulate the Behavior of Uniform Autonomous Bilateral Networks and Rings of Moore Automata

It is shown that it is possible to use unilateral rings to simulate the behavior of arbitrary uniform autonomous bilateral networks and rings of Moore automata in the sense that $a_i(t)=\Psi[\delta_{(i+t)\operatorname{mod} n}(2t)]$, where $a_i(t)$ is the state of the $i$-th automaton in a network at the instant $t$; $\delta_j(2t)$ is the state of the $j$-th automaton in a ring at the instant $2t$; and $\Psi$ is some function.