Authors: Christiane Frougny ¹; Anna Chiara Lai ²

• 1 Laboratoire d'informatique Algorithmique : Fondements et Applications
• 2 Dipartimento di Scienze di Base e Applicate per l'Ingegneria

We study expansions in non-integer negative base -beta introduced by Ito and Sadahiro. Using countable automata associated with (-beta)-expansions, we characterize the case where the (-beta)-shift is a system of finite type. We prove that, if beta is a Pisot number, then the (-beta)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer. We then give an on-line algorithm for the conversion from positive base beta to negative base -beta. When beta is a Pisot number, the conversion can be realized by a finite on-line transducer.