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We consider numeration systems where the base is a negative integer, or a complexnumber which is a root of a negative integer. We give parallel algorithms for additionin these numeration systems, from which we derive on-line algorithms realized by finiteautomata. A general construction relating addition in base fi and addition in base fimisgiven. Results on addition in base fi =mpb, where b is a relative integer, follow. We alsoshow that addition in base the golden ratio is...

On-line finite automata for addition in some numeration systems