Geodesic
Graphs of Linear Operators
Informatics and Automation, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 64-71 
A. I. Garber. Graphs of Linear Operators. Informatics and Automation, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 64-71. http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a4/
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In 2006 the author proposed an algorithm for constructing graphs of difference operators. In this paper, the following question is studied: to which linear operators $\mathcal A$ does this algorithm apply? Graphs of difference operators are used to determine the complexity of a sequence in the sense of Arnold, so the algorithm makes it possible to determine the complexity of any sequence.

[1] Uspenskii V., Vereschagin N., Shen A., Kolmogorovskaya slozhnost, E-print , 2004 http:// lj.streamclub.ru/books/complex/uspen.ps

[2] Arnold V. I., Slozhnost konechnykh posledovatelnostei nulei i edinits i geometriya konechnykh funktsionalnykh prostranstv, E-print , 2005 http:// mms.math-net.ru/meetings/2005/arnold.pdf

[3] Arnold V. I., “Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions”, Funct. Anal. and Other Math., 1:1 (2006), 1–15 | DOI | MR

[4] Arnold V. I., Slozhnost konechnykh posledovatelnostei nulei i edinits i geometriya konechnykh funktsionalnykh prostranstv, Lektsiya 13.05.2006 g. BKZ Akad. RAN http:// elementy.ru/lib/430178/430281

[5] Garber A. I., “Graphs of difference operators for $p$-ary sequences”, Funct. Anal. and Other Math., 1:2 (2006), 159–173 | DOI | MR | Zbl

[6] Karpenkov O. N., “On examples of difference operators for $\{0,1\}$-valued functions over finite sets”, Funct. Anal. and Other Math., 1:2 (2006), 175–180 | DOI | MR | Zbl