The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with critical exponent $\leq 7/3$. The same conclusion holds for Fibonacci-automatic and Tribonacci-automatic sequences.

翻译：无限词 $\bf x$ 的临界指数是所有有限非空因子 $f$ 的指数之上确界。本文证明对于所有整数 $k\geq 2$，存在临界指数 $\leq 7/3$ 的二进制无限 $k$-自动序列。该结论同样适用于斐波那契自动序列与特里波纳奇自动序列。