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

TL;DR

This paper explores the concept of a 'state' in distributed computational structures within dynamic environments, proposing a model and examining its implications for understanding computational equivalence.

Contribution

It introduces a novel model for the state of distributed computational structures in dynamic environments and analyzes its theoretical implications.

Findings

Defines a new concept of state for distributed structures

Establishes corollaries related to the model

Provides a framework for comparing computational structures

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.