A state of a dynamic computational structure distributed in an environment: a model and its corollaries

Abstract: Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial computation and space-time crystallography. For any computational model it is natural to define a functional equivalence of different but related computational structures. In the finite automata theory an example of such equivalence is automata homomorphism and, in particular, automata isomorphism. If we continue to stick to the finite automata theory, a fundamental question arise, what a state of a distributed computational structure is. This work is devoted to particular solution of the issue.