English

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

R2 v1 2026-06-23T04:17:51.433Z