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Graphs of linear operators. (English. Russian original) Zbl 1196.11035
Proc. Steklov Inst. Math. 263, 57-64 (2008); translation from Tr. Mat. Inst. Steklova 263, 64-71 (2008).
Summary: In 2006, the author proposed an algorithm for constructing graphs of difference operators [Funct. Anal. Other Math. 1, No. 2, 159–173 (2006; Zbl 1151.11306)]. 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 V. I. Arnold [Funct. Anal. Other Math. 1, No. 1, 1–15 (2006; Zbl 1196.11033)]. So, the algorithm makes it possible to determine the complexity of any sequence.

##### MSC:
 11B50 Sequences (mod $$m$$) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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##### References:
 [1] V. Uspenskii, N. Vereshchagin, and A. Shen’, ”Kolmogorov Complexity,” http://lj.streamclub.ru/books/complex/uspen.ps [2] V. I. Arnold, ”Complexity of Finite Sequences of Zeros and Ones and Geometry of Finite Spaces of Functions,” http://mms.math-net.ru/meetings/2005/arnold.pdf [3] V. I. Arnold, ”Complexity of Finite Sequences of Zeros and Ones and Geometry of Finite Spaces of Functions,” Funct. Anal. Other Math. 1(1), 1–15 (2006). · Zbl 1196.11033 [4] V. I. Arnold, ”Complexity of Finite Sequences of Zeros and Ones and Geometry of Finite Spaces of Functions (Lecture at the Great Concert Hall ”Academic,” Russian Academy of Sciences, May 13, 2006),” http://elementy.ru/lib/430178/430281 [5] A. I. Garber, ”Graphs of Difference Operators for p-ary Sequences,” Funct. Anal. Other Math. 1(2), 159–173 (2006). · Zbl 1151.11306 [6] O. N. Karpenkov, ”On Examples of Difference Operators for {0, 1}-Valued Functions over Finite Sets,” Funct. Anal. Other Math. 1(2), 175–180 (2006). · Zbl 1196.11036
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