An order-preserving property of additive invariant for Takesue-type reversible cellular automata

Abstract

We show that, for a fairly large class of reversible, one-dimensional cellular automata, the set of additive invariants exhibits an algebraic structure. More precisely, if $f$ and $g$ are one-dimensional, reversible cellular automata of the kind considered by Takesue, we show that there is a binary operation on these automata $\vee$ such that $\psi (f)\subseteq \psi (f\vee g)$, where $\psi (f)$ denotes the set of additive invariants of $f$ and $\subseteq$ denotes the inclusion relation between real subspaces.

11 pages

References in corpus (1)

• A "No-Go" Theorem for the Existence of an Action Principle for Discrete Invertible Dynamical Systems