Automatic \(\beta\)-expansions of formal Laurent series over finite fields (Q2253090)

The classical setting of the \(\beta\)-expansions of real numbers has been studied when, for instance, the base \(\beta\) is a Pisot or a Salem number. In this very interesting paper, the authors deal with another setting, that of the \(\beta\)-expansions of formal Laurent series over finite fields. They extend a well-known theorem of Christol to this setting. Their main result is that given a Pisot or a Salem base series \(\beta\) and a formal Laurent series \(\alpha\), the \(\beta\)-expansion of \(\alpha\) is automatic if and only of \(\alpha\) is algebraic. The analogue of this result in the classical setting is false.