On Negative Bases

Abstract. We study expansions in non-integer negative base - introduced by Ito and Sadahiro [7]. Using countable automata associated with (-)-expansions, we characterize the case where the (-)-shift is a system of finite type. We prove that, if is a Pisot number, then the (-)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer.

• Type: Journal
• Year: 2009
• Where: DLT
• Authors: Christiane Frougny, Anna Chiara Lai
• Keywords: Countable Automata, DLT 2009, Non-integer Negative Base, Sofic System, Theoretical Computer Science