On Nilpotency and Asymptotic Nilpotency of Cellular Automata
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 SZd 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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.