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...f the longest discriminating string that differentiates the between the behavior of two distinct states. As an example, consider the square-free bi-infinite ternary sequence introduced by Kurosaki in =-=[10]-=-. The bi-infinite sequence is obtained by iterating the map ϕ(x) = xx̂x where x is defined by the substitution x[0 ↦→ 1,1 ↦→ 0] and ̂x □ 90 1 0 2 1 01 7 1 1 0 3 1 1 6 0 4 1 5 0 0 Figure 1: The machin...

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...rmore, she showed that this was optimal over a ternary alphabet. In 2001, Klepinin and Sukhanov [4] examined Arshon’s word in more depth and showed that it also avoided 7/4+-powers. In 2008, Kurosaki =-=[5]-=- gave a new construction of a squarefree word. In this short note, we show that Kurosaki’s word also avoids 7/4+-powers. Let us now recall some basic definitions. Let Σ be a finite alphabet and let x ...