Conservation laws in cellular automata

@article{Pivato2002ConservationLI,
  title={Conservation laws in cellular automata},
  author={M. Pivato},
  journal={Nonlinearity},
  year={2002},
  volume={15},
  pages={1781-1793}
}
  • M. Pivato
  • Published 2002
  • Mathematics
  • Nonlinearity
  • If is a discrete Abelian group and a finite set, then a cellular automaton (CA) is a continuous map :? that commutes with all -shifts. If :?, then, for any a, we define ?(a) = ?x(ax) (if finite); is conserved by if ? is constant under the action of . 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. 
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