[en] We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root beta>1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number beta.
Disciplines :
Computer science Mathematics
Author, co-author :
Charlier, Emilie ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rampersad, Narad ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Waxweiler, Laurent ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Structure of the minimal automaton of a numeration language
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