## Christiane Frougny ; Anna Chiara Lai - Negative bases and automata

dmtcs:538 - Discrete Mathematics & Theoretical Computer Science, April 11, 2011, Vol. 13 no. 1 - https://doi.org/10.46298/dmtcs.538
Negative bases and automata

Authors: Christiane Frougny ; Anna Chiara Lai

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.

Volume: Vol. 13 no. 1
Section: Automata, Logic and Semantics
Published on: April 11, 2011
Submitted on: December 10, 2010
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]