Revision of asymptotic behavior of the complexity of word assembly by concatenation circuitsстатья
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Аннотация:The problem of the complexity of word assembly is studied.
The complexity of the word refers to the minimum number of
concatenation operations
sufficient to obtain this word on the basis of one-letter
words over a finite alphabet $A$ (repeated use of the received words is
permitted).
Let $L_A^c(n)$ be maximum complexity of words of length~$n$
over a finite alphabet $A$. In this paper, we establish 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).
$