Automaticity and invariant measures of linear cellular automata

  title={Automaticity and invariant measures of linear cellular automata},
  author={Eric S. Rowland and Reem Yassawi},
  • Eric S. Rowland, Reem Yassawi
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • We show that spacetime diagrams of linear cellular automata $\Phi$ with $(-p)$-automatic initial conditions are automatic. This extends existing results on initial conditions which are eventually constant. Each automatic spacetime diagram defines a $(\sigma, \Phi)$-invariant set in ${\mathbb F}_p^{\mathbb Z}$, where $\sigma$ is the left shift map, and if the initial condition is not eventually periodic then this invariant set is nontrivial. We also construct, for the Ledrappier cellular… CONTINUE READING

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