Conservation laws in cellular automata
Marcus Pivato Β· Nonlinearity Β· 2002
If π is a discrete Abelian group and π a finite set, then a cellular automaton (CA) is a continuous map π:π π βπ π that commutes with all π-shifts. If Ο:πββ, then, for any a βπ π , we define Ξ£Ο( a ) = β x βπ Ο( a x ) (if finite); Ο is conserved by π if Ξ£Ο is constant under the action of π. We characterize such conservation laws in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.