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Abstract
In this article, we construct a family of infinite words, generated by countable automata and also generated by substitutions over infinite alphabets, closely related to parenthesis languages and we study their complexity functions. We obtain a family of binary infinite words m ( b ) , indexed on the number b ≥ 1 of parenthesis types, such that the growth order of the complexity function of m ( b ) is n ( log n ) 2 if b = 1 and n 1 + log 2 b b if b ≥ 2 .
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