Stable Multi-Level Monotonic Eroders

TL;DR

This paper characterizes one-dimensional monotonic cellular automata that reliably erase finite nonzero states even with random noise, extending classical results to noisy environments.

Contribution

It provides a new combinatorial characterization for noisy eroders, advancing understanding of cellular automata robustness.

Findings

Characterization of noisy eroders achieved

Extension of classical eroder theory to stochastic settings

Foundational results for designing robust cellular automata

Abstract

Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal'perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.