In Case 2 of the proof of Proposition 3.7 we consider a conjugate of w and write it as YZYZ' with |Z| > |Z'|. Then, using the definition of a psi_n-kernel repetition, we get the inequality (n-1)(|YZY|+1) >= n|YZ| - 3. To correctly obtain this inequality requires |YZY| >= |X|; our error is that this does not hold when X begins and ends at even positions of the word. In this case, we instead have only |YZY| = |X| - 1, and the previous inequality is short by n-1. This error was pointed out by Alex Gu, who also gives an easy fix: Lemma 3.5 gives M | |YZ|. Once YZ' in ker(psi_n) has been established, it also gives M | |YZ'|. Since |Z| > |Z'|, this forces |Z| >= |Z'| + M and the missing n-1 is recovered whenever M >= n-1. In the range considered in the paper this is immediate: n <= 6m+8 gives n-1 <= 6m+7, while 6m+7 <= 4^(m-2) = M for m >= 7.
- In the discussion following Corollary 5 on p. 1376 and again in the "Final Thoughts" section on p. 1378, we compare our automaticity bounds from Corollary 5 with some results from the paper J. Shallit, Automaticity IV: sequences, sets, and diversity, J. Theorie Nombres Bordeaux 8 (1996), 347-367. Unfortunately, the comparisons between our results and Shallit's are not valid, because our paper uses most-significant-digit-first representation and his uses least-significant-digit-first representation.
- The words "legal" and "valid" should be exchanged in the last paragraph of Lemma 7 on p. 604.
- Lemma 3(1) should read "h(\Phi(\beta S)) is a prefix of h(\Phi(\beta L)) and h(\Phi^2(\beta S)) is a prefix of h(\Phi^2(\beta L))" and the first paragraph of the proof should be modified accordingly.
- In the proof of Lemma 3, the first sentence of the second paragraph should read, "Since h(S) is a suffix of h(L), \overline(h(S)) is a suffix of h(SL), and so \overline(h(SL)) is a suffix of h(SLL)."
- in Lemma 1, instead of a,b,c \in \Sigma, it should be a,c \in \Sigma, b \in \Sigma^*
- in the proof of Lemma 5 (twice), the proof of Theorem 6, and the example: (k-2)(N-2+mk\Delta) should be instead (k-1)(N-2+mk\Delta).
- In the first paragraph of Section 4, we state that for a uniform morphism h, if a word is markable then its extensions are markable. Wojciech Wegrzynek has pointed out to us that this claim is not correct. However, he has also shown that it becomes correct with the additional condition that h(0) and h(1) end with different letters. Since this is the case for all morphisms h_n that are used in the paper, the results remain correct.