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On the successor function in non-classical numeration systems

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STACS 96 (STACS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1046))

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Abstract

Let U be a strictly increasing sequence of integers, and let L(U) be the set of greedy U-representations of all the nonnegative integers. The successor function maps the greedy U-representation of N onto the greedy U-representation of N+1. We show that the successor function associated to U is computable by a finite 2-tape automaton if and only if the set L(U) is recognizable by a finite automaton.

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Authors and Affiliations

  1. Institut Blaise Pascal, Université Paris 8 and Laboratoire Informatique Théorique et Programmation, 4 place Jussieu, 75252, Paris Cedex 05, France

    Christiane Frougny

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  1. Christiane Frougny
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Claude Puech Rüdiger Reischuk

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© 1996 Springer-Verlag Berlin Heidelberg

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Frougny, C. (1996). On the successor function in non-classical numeration systems. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_44

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  • DOI: https://doi.org/10.1007/3-540-60922-9_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60922-3

  • Online ISBN: 978-3-540-49723-3

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