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On-line finite automata for addition in some numeration systems

Published online by Cambridge University Press:  15 August 2002

Christiane Frougny
Christiane Frougny*
Affiliation:
Université Paris VIII and L.I.A.F.A., Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France; Christiane.Frougny@liafa.jussieu.fr.
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Abstract

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 $\beta=\sqrt[m]{b}$, 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.

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 1 , January 1999 , pp. 79 - 101
Copyright
© EDP Sciences, 1999

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