Cellular automaton created as an m-ary product of algebraic quasi-multiautomata

In this work, we follow the construction of an n-ary system of Cartesian composition of multiautomata with internal links, where we define the internal links to the homogeneous and heterogeneous products of multi-automata. While the introduction of an internal link is rectilinear in the Cartesian composition, it requires a new approach in product construction for the other two automata products. In this way, it is possible to focus on multiple options for creating these systems. More specifically, we combine automata and multi-automata with binding according to the basic definitions given by Dörfler. This approach shows new connections to cellular automata, which allow for the modeling of phenomena in many areas. At the end of the work, we discuss the advantages of these individual schemes for quasi-multiautomata connections. https://link.springer.com/article/10.1007/s00500-022-07747-9