On the supports of recognizable series over a field and a single letter alphabet

Guillaume Chapuy (1) , Ines Klimann (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We prove that the support of a recognizable series over a field of characteristic zero and a single letter alphabet is recognizable. This provides an answer to a question of Kirsten (2009). Then we give an example of a recognizable series over a field of prime characteristic and a single letter alphabet whose support is not recognizable which provides an answer to a question of Kirsten and Quaas (2011).

Keywords: Formal languages; Recognizable series; Support of series

Domains: Computer Science [cs]; Formal Languages and Automata Theory [cs.FL]

Guillaume Chapuy, Ines Klimann. On the supports of recognizable series over a field and a single letter alphabet. Information Processing Letters, 2011, 111 (23-24), pp.1096-1098. ⟨10.1016/j.ipl.2011.09.010⟩. ⟨hal-00663147⟩