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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1998: STACS 98 pp 356–365Cite as

Radix representations of algebraic number fields and finite automata

  • Automata and Formal Languages II
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

Abstract

Let L be the set of algebraic integers of a number field Q[-γ]. Let β ⊂ L and let A and D be two finite subsets of L with 0 ∈ D. Assume that β and all its conjugates have moduli greater than one. Denote by v : A* → D* the normalization relation which maps any representation of an algebraic integer in base β with digits in A onto the ones of the same number with digits in D. In this case, the relation v is shown to be computable by a right finite state automaton. If (β, D) is a valid number system, then the normalization v is a right sub-sequential function. We also prove that the question whether (β, D) does or does not give a valid number system for L can be decided by executing a finite number of arithmetical operations.

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Authors and Affiliations

  1. LIAFA, Université Paris 7, 2 place Jussieu, 75252, Paris Cedex 05, France

    Taoufik Safer

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  1. Taoufik Safer
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Safer, T. (1998). Radix representations of algebraic number fields and finite automata. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028574

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  • DOI: https://doi.org/10.1007/BFb0028574

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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