A decision problem for ultimate periodicity in non-standard numeration systems
Charlier, Emilie[Université Libre de Bruxelles - ULB > Département de mathématique > Géométrie, Théorie des groupes et Combinatoire > >]
Journées de l'ANR SubTile, Decidability problems for substitutive sequences, tilings and numerations,
du 2 juillet 2012 au 4 juillet 2012
[en] numeration system ; decidability question ; state complexity ; ultimately periodic set
[en] In the first part of the talk, I will overview some results on state complexity of ultimately periodic sets in various numeration systems. In the second part of the talk, I will present some applications of these methods to the following decidability question: given a DFA recognizing a set of integers represented in a fixed numeration system, decide whether this set is ultimately periodic. The techniques presented in this talk could be extended to other classes of sets of integers, and thus, could be applied to new decidability questions.