On the successor function in non-classical numeration systems

  • Christiane Frougny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


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.


Terminal State Finite Index Finite Automaton Successor Function Numeration System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Christiane Frougny
    • 1
  1. 1.Institut Blaise PascalUniversité Paris 8 and Laboratoire Informatique Théorique et ProgrammationParis Cedex 05France

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