On the supports of recognizable series over a field and a single letter alphabet
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) [4]. 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) [5]. (C) 2011 Elsevier B.V. All rights reserved.
recognizable series formal languages support of series