An order-preserving property of additive invariant for Takesue-type reversible cellular automata
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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 $ψ(f)\subseteq ψ(f\vee g)$, where $ψ(f)$ denotes the set of additive invariants of $f$ and $\subseteq$ denotes the inclusion relation between real subspaces.
11 pages
11 pages