Automaticity and invariant measures of linear cellular automata

@article{Rowland2018AutomaticityAI,
  title={Automaticity and invariant measures of linear cellular automata},
  author={Eric S. Rowland and Reem Yassawi},
  journal={ArXiv},
  year={2018},
  volume={abs/1811.01256}
}
  • 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

    Figures and Topics from this paper.

    Explore Further: Topics Discussed in This Paper