On-line finite automata for addition in some numeration systems

@article{Frougny1999OnlineFA,
  title={On-line finite automata for addition in some numeration systems},
  author={Christiane Frougny},
  journal={ITA},
  year={1999},
  volume={33},
  pages={79-101}
}
We consider numeration systems where the base is a negative integer, or a complex number which is a root of a negative integer. We give parallel algorithms for addition in these numeration systems, from which we derive on-line algorithms realized by finite automata. A general construction relating addition in base β and addition in base β is given. Results on addition in base β = m √ b, where b is a relative integer, follow. We also show that addition in base the golden ratio is computable by… CONTINUE READING

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