Generalization of stable cellular automata reveals complexities in Sturmian words, suggesting unique properties.
In this paper, we generalize the study of some class of cellular automata (CA) preserving stability, called stable cellular automata (SCA) on Sturmian words. After establishing the classic complexity of obtained words by these SCA, their special factors are also specified. Next, we prove that their palindromic complexity is 1 or 2. Finally, we show that these words are balanced and establish their abelian complexity.
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Barro et al. (2025) studied this question.
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