Meta transitions in computers

Paper [1] proposes a general method for generating an infinite sequence of automata: $\textrm{FA} \xrightarrow{deconvolution} \textrm{IFA} \xrightarrow{convolution} \textrm{FA} \xrightarrow{deconvolution} \textrm{IFA} \xrightarrow{convolution} {\dots}$, where FA is a finite automaton, and IFA is an infinite automaton. This study presents an example where a simple $\bar{x}|\bar{q}_{(4)} $ device is the primary finite automaton. Its main computable function is an identity map. It was found that the generated main sequence of finite automata and its side branches contain many known functions. Moreover, as we move along the sequence to the right to infinity, there are many entities still not used in mathematics, although we have some general notions. Note that the finite elements in this sequence are specified as computational devices suitable for theoretical research, hardware implementation, and the creation of B-computers [6]. The key meta-operations applied to the elements of the sequence are deconvolution and convolution.