Von Neumann regularity, split epicness and elementary cellular automata
Formal Languages and Automata Theory
2018-10-11 v3 Dynamical Systems
Cellular Automata and Lattice Gases
Abstract
We show that a cellular automaton on a mixing subshift of finite type is a Von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from [S.-T\"orm\"a, 2015] that Von Neumann regularity is decidable condition, and we decide it for all elementary CA.
Keywords
Cite
@article{arxiv.1804.03913,
title = {Von Neumann regularity, split epicness and elementary cellular automata},
author = {Ville Salo},
journal= {arXiv preprint arXiv:1804.03913},
year = {2018}
}
Comments
12 pages + appendix, 6 figures. The Python scripts for checking the rules are included as ancillary files. Fixed some typos in this version. Comments welcome!