On Nilpotency and Asymptotic Nilpotency of Cellular Automata
arXiv:1205.6714 · doi:10.4204/EPTCS.90.7
Abstract
We prove a conjecture of P. Guillon and G. Richard by showing that cellular automata that eventually fix all cells to a fixed symbol 0 are nilpotent on S^Z^d for all d. We also briefly discuss nilpotency on other subshifts, and show that weak nilpotency implies nilpotency in all subshifts and all dimensions, since we do not know a published reference for this.
In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498