Computability by finite automata and pisot bases

@article{Berend1994ComputabilityBF,
  title={Computability by finite automata and pisot bases},
  author={Daniel Berend and Christiane Frougny},
  journal={Mathematical systems theory},
  year={1994},
  volume={27},
  pages={275-282}
}
We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.