Note: An order-preserving property of additive invariants for Takesue-type reversible cellular automata

Authors:
Gianluca Caterina;Bruce Boghosian
Affiliations:
-;-
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

We show that, for a large and important 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 (1989) [1], we show that the component-wise maximum @? on these automata is such that @j(f)@?@j(f@?g), where @j(f) denotes the set of additive invariants of f and @? denotes the inclusion relation between real subspaces.