Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 2, Pages 12–18 (Mi vmumm130)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Revision of asymptotic behavior of the complexity of word assembly by concatenation circuits

V. V. Kocherginab, D. V. Kochergina

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Lomonosov Moscow State University, Bogoliubov Institute for Theoretical Problems of Microphysics
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Abstract: 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). $
Key words: concatenation circuits, word chains, circuits complexity, Shannon function.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00598
Received: 29.05.2015
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 2, Pages 55–60
DOI: https://doi.org/10.3103/S0027132216020029
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: V. V. Kochergin, D. V. Kochergin, “Revision of asymptotic behavior of the complexity of word assembly by concatenation circuits”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 12–18; Moscow University Mathematics Bulletin, 71:2 (2016), 55–60
Citation in format AMSBIB
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