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Linear numeration systems, θ-developments and finite automata

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STACS 89 (STACS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 349))

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Abstract

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.

This research has been partly supported by the Programme de Recherches Coordonnées Mathématiques et Informatique.

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Authors and Affiliations

  1. UER de Mathématiques et Informatique, LITP and Université René Descartes, 12, Rue Cujas, 75005, Paris, France

    Christiane Frougny

Authors
  1. Christiane Frougny
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B. Monien R. Cori

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© 1989 Springer-Verlag Berlin Heidelberg

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Frougny, C. (1989). Linear numeration systems, θ-developments and finite automata. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028980

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  • DOI: https://doi.org/10.1007/BFb0028980

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50840-3

  • Online ISBN: 978-3-540-46098-5

  • eBook Packages: Springer Book Archive

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