Representation of numbers in nonclassical numeration systems
نویسنده
چکیده
Numeration systems the basis of which is defined b y a linear recurrence with integer coeficients are considered. W e give conditions on the recurrence under which the function of normalization which transforms any representation of an integer into the normal one obtained by the usual algorithm can be realized b y a finite automaton. Addition i s a particular case of normalization. The same questions are discussed for the representation of real numbers in basis 8 , where 8 is a real number > 1. In particular it is shown that if 8 is a Pisot number, then the normalization and the addition in basis 8 are computable by a finite automaton.
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