An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata

TL;DR

This paper investigates how one-dimensional elementary cellular automata maintain their behavior under asynchronous updates, using a statistical experimental approach to identify which automata are robust to asynchronism.

Contribution

It introduces a new experimental protocol to evaluate the robustness of 1D elementary CA to asynchronism and provides guidelines for selecting models based on robustness criteria.

Findings

Identified which 1D elementary CA are robust to asynchronism.

Developed a statistical method to measure CA behavior under asynchronous updates.

Provided insights for modeling complex systems with asynchronous dynamics.

Abstract

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by ``the behavior of CA is robust to asynchronism'' using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.