Geodesic
Revision of asymptotic behavior of the complexity of word assembly by concatenation circuits
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 12-18 
V. V. Kochergin; D. V. Kochergin. Revision of asymptotic behavior of the complexity of word assembly by concatenation circuits. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 12-18. http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a1/
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     author = {V. V. Kochergin and D. V. Kochergin},
     title = {Revision of asymptotic behavior of the complexity of word assembly by concatenation circuits},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of complexity of word assembly is studied. The complexity of a word means the minimal number of concatenation operations sufficient to obtain this word in the basis of one-letter words over a finite alphabet $A$ (repeated use of obtained words is permitted). Let $L_A^c(n)$ be the maximum complexity of words of length $n$ over a finite alphabet $A$. In this paper we prove that $ L_A^c(n) = \frac n {\log_{|A|} n} \left( 1 + (2+o(1)) \frac {\log_2 \log_2 n}{\log_2 n} \right). $

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