| Issue |
RAIRO-Theor. Inf. Appl.
Volume 33, Number 1, January Fabruary 1999
|
|
|---|---|---|
| Page(s) | 79 - 101 | |
| DOI | https://doi.org/10.1051/ita:1999107 | |
| Published online | 15 August 2002 | |
On-line finite automata for addition in some numeration systems
Université Paris VIII and
L.I.A.F.A., Case 7014, 2 place Jussieu, 75251
Paris Cedex 05, France;
Christiane.Frougny@liafa.jussieu.fr.
Received:
May
1998
Accepted:
November
1998
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 βm is given.
Results on addition in base ![$\beta=\sqrt[m]{b}$](/articles/ita/abs/1999/01/ita9906/ita9906_tex_eq2.png)
, where b is a relative
integer, follow.
We also show that addition in base the golden ratio
is computable by an on-line finite automaton, but is not
parallelizable.
© EDP Sciences, 1999
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