Linear numeration systems, θ-developments and finite automata

  • Christiane Frougny
Contributed Papers Automata Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 349)


In numeration systems defined by a linear recurrence relation, as well as in the set of developments of numbers in a non integer basis ϑ, we define the notion of normal representation of a number. We show that, taking for ϑ the greatest root of the characteristic polynomial of the linear recurrence, and under certain conditions of confluence, the normal representation can be obtained from any representation by a finite automaton which is the composition of two sequential transducers derived from the linear recurrence. The addition of two numbers can be performed by a left sequential transducer.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Christiane Frougny
    • 1
  1. 1.UER de Mathématiques et InformatiqueLITP and Université René DescartesParisFrance

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