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.
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Frougny, C., Lai, A.C. (2009). On Negative Bases. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_20
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DOI: https://doi.org/10.1007/978-3-642-02737-6_20
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