Numeration Systems on a Regular Language

Numeration Systems on a Regular Language

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...

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Veröffentlicht in:Theory of computing systems 2000-02, Vol.34 (1), p.27-44
Hauptverfasser: Lecomte, P. B. A., Rigo, M.
Format: Artikel
Sprache:eng
Schlagworte:
Automation
Computation
Constants
Mathematical analysis
Multiplication
Order disorder
Recognition
Translations
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Zusammenfassung: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.
ISSN:1432-4350
1433-0490
DOI:10.1007/s002240010014