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Fibonacci numeration systems and rational functions

  • Christiane Frougny
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 233)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Christiane Frougny
    • 1
  1. 1.Université René Descartes and L.I.T.PParis

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