A collective of stateless automata in a $n$-dimensional environment as a distributed dynamic automaton-like object: a model and its corollaries

TL;DR

This paper models a collective of stateless automata in an n-dimensional environment as a dynamic automaton-like object, proposing a relativity-based approach to defining its state and exploring its properties.

Contribution

It introduces a novel model of a distributed automaton-like object with a relativity-based state definition in an n-dimensional environment.

Findings

A new approach to defining state in distributed automata

Modeling of automaton-like objects in high-dimensional spaces

Implications for distributed computation and automata theory

Abstract

In this work a collective of interacting stateless automata in a discrete geometric $n$-dimenstional environment is considered as an integral automaton-like computational dynamic object. For such distributed on the environment object different approaches to definition of the measure of state transition are possible. We propose an approach for defining what a state is. The approach is based on the concept of relativity in Poincar\'e's interpretation.