We study expansions in non-integer negative base -β introduced by Ito and Sadahiro [7]. Using countable automata associated with (β)-expansions, we characterize the case where the (;β)-shift is a system of finite type. We prove that, if β is a Pisot number, then the (;β)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer. © 2009 Springer Berlin Heidelberg.
On negative bases / Frougny, Christiane; LAI, ANNA CHIARA. - 5583:(2009), pp. 252-263. (Intervento presentato al convegno 13th International Conference on Developments in Language Theory, DLT 2009 tenutosi a Stuttgart; Germany nel 2009) [10.1007/978-3-642-02737-6_20].
On negative bases
LAI, ANNA CHIARA
2009
Abstract
We study expansions in non-integer negative base -β introduced by Ito and Sadahiro [7]. Using countable automata associated with (β)-expansions, we characterize the case where the (;β)-shift is a system of finite type. We prove that, if β is a Pisot number, then the (;β)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer. © 2009 Springer Berlin Heidelberg.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
