We show that a sequence satisfying a certain symmetry property is 2-regular in the sense of Allouche and Shallit. We apply this theorem to develop a general approach for studying the ℓ-abelian complexity of 2-automatic sequences. In particular, we prove that the period-doublingword and the Thue–Morse word have 2-abelian complexity sequences that are 2-regular. Along the way, we also prove that the 2-block codings of these two words have 1-abelian complexity sequences that are 2-regular.
نوع الوثيقة:
conferencePaper
اللغة:
English
العلاقة:
Journées montoises d'informatique théorique, Nancy, France (23/09/2014 - 26/09/2014)
