Geodesic
The Shannon function of computation of the Arnold complexity of length $2^n$ binary words
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 6, pp. 49-55.

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A method for the fast computation of the Arnold complexity of length $2^n$ binary words has been recently proposed by the author. Based on this method, an exact value of the Shannon function is obtained for almost all $n$. Bibliogr. 5.
Keywords: binary word, word complexity, Arnold complexity, Shannon function. 
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Yu. V. Merekin. The Shannon function of computation of the Arnold complexity of length $2^n$ binary words. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 6, pp. 49-55. http://geodesic.mathdoc.fr/item/DA_2012_19_6_a4/

[1] Arnold V. I., “Topologiya i statistika formul arifmetiki”, Uspekhi mat. nauk, 58:4 (2003), 3–28 | DOI | MR | Zbl

[2] Merekin Yu. V., “O vychislenii slozhnosti po Arnoldu dvoichnykh slov”, Mat. XVI Mezhdunar. konf. “Problemy teoreticheskoi kibernetiki” (Nizhnii Novgorod, 20–25 iyunya 2011 g.), Izd-vo Nizhegorodsk. gos. un-ta, Nizhnii Novgorod, 2011, 315–319

[3] Merekin Yu. V., “On the computational complexity of the Arnold complexity of binary words”, Asian-Eur. J. Math., 2:4 (2009), 649–656 | MR | Zbl

[4] Merekin Yu. V., “On the computation of Arnold complexity of length $2^n$ binary words”, Asian-Eur. J. Math., 4:2 (2011), 295–300 | DOI | MR | Zbl

[5] Merekin Yu. V., Fast computation of the Arnold complexity of length $2^n$ binary words, ArXive e-print, 2012, arXiv: 1209.4700[math.CO]