Geodesic
Orders of growth of Shannon functions for circuit complexity over infinite bases
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 55-57

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It is shown that any function of one real variable being composition of rational functions with real coefficients, logarithms, and exponents and having an order of growth between $n$ and $2^{O(n^{1/2})}$ is an order of growth of the Shannon function for the circuit complexity over a certain infinite basis. 
@article{VMUMM_2013_3_a8,
     author = {O. M. Kasim-zade},
     title = {Orders of growth of {Shannon} functions for circuit complexity over infinite bases},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--57},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/}
}
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O. M. Kasim-zade. Orders of growth of Shannon functions for circuit complexity over infinite bases. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a8/