Negative bases and automata
(1012.3721)Abstract
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.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.