Abstract
In the Fibonacci numeration system of order m (m integer ≥2), every integer has a unique canonical representation which has no run of m consecutive l's. We show that this canonical representation can be obtained from any representation by a rational function, which is the composition of two subsequential functions that are simply obtained from the system. The addition of two integers represented in this system can be performed by a subsequential machine. The conversion from a Fibonacci representation to a standard binary representation (or conversely) cannot be realized by a finite-state machine.
This research has been partly supported by the Programme de Recherches Coordonnées Mathématiques et Informatique of the Ministère de la Recherche et de la Technologie.
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© 1986 Springer-Verlag Berlin Heidelberg
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Frougny, C. (1986). Fibonacci numeration systems and rational functions. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016259
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DOI: https://doi.org/10.1007/BFb0016259
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