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Recognizability of substitutions and complexity of automatic sequences. (Reconnaissabilité des substitutions et complexité des suites automatiques.) (French) Zbl 0855.68072

Summary: We first recall some notions and one theorem of recognizability about infinite words fixed points of primitive substitutions. When the length of the substitution is constant equal to \(q\), we study the complexity function \(p(n)\) of the fixed point \(u\), which is the number of factors of \(u\) of length \(n\). We give a method to compute \(p(n)\) with linear recurrence formulas and we prove that the sequence \((p(n + 1) - p(n))_{n \in \mathbb{N}}\) is \(q\)-automatic.

MSC:

68R15 Combinatorics on words
68Q45 Formal languages and automata

Keywords:

recognizability
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References:

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