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$\bf x$的临界指数是指所有有限非空因子$f$的指数上确界。本文证明，对于所有整数$k\geq 2$，存在一个二元无限$k$-自动序列，其临界指数$\leq 7/3$。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。