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Numeration Systems on a Regular Language

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Abstract.

Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the lexicographic ordering. For these systems of numeration, we show that ultimately periodic sets are recognizable. We also study translation and multiplication by constants as well as the order-dependence of the recognizability.

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Authors and Affiliations

  1. Institut de Mathématiques,\{plecomte,M.Rigo\}@ulg.ac.be, Université de Liège,Grande Traverse 12 (B 37), B-4000 Liège, Belgium, BE

    P. B. A. Lecomte & M. Rigo

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  1. P. B. A. Lecomte
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  2. M. Rigo
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Received March 12, 1999. Online publication December 4, 2000.

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Lecomte, P., Rigo, M. Numeration Systems on a Regular Language. Theory Comput. Systems 34, 27–44 (2000). https://doi.org/10.1007/s002240010014

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  • DOI: https://doi.org/10.1007/s002240010014

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