Normality and finite-state dimension of Liouville numbers (Q285510)

The paper presents, for a given base \(b\geq2\), a new construction of a Liouville number which is normal to the base \(b\). The construction is combinatorial and uses on the one hand an argument similar to \textit{E. Maillet}'s [C. R. Acad. Sci., Paris 138, 410--411 (1904; JFM 35.0232.02)] for proving the Liouville property and on the other hand an infinite concatenation of de Bruijn words for normality. Then, by diluting the expansions, the authors show that for every rational \(r\), \(0\leq r\leq 1\), there is a Liouville number having finite-state dimension \(r\).