Stable Multi-Level Monotonic Eroders
Probability
2018-09-26 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1809.09503,
title = {Stable Multi-Level Monotonic Eroders},
author = {Péter Gács and Ilkka Törmä},
journal= {arXiv preprint arXiv:1809.09503},
year = {2018}
}
Comments
32 pages, 9 figures