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Graphs of linear operators

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Abstract

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.

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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

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Authors and Affiliations

  1. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. I. Garber

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  1. A. I. Garber
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Correspondence to A. I. Garber.

Additional information

Original Russian Text © A.I. Garber, 2008, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 64–71.

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Garber, A.I. Graphs of linear operators. Proc. Steklov Inst. Math. 263, 57–64 (2008). https://doi.org/10.1134/S0081543808040056

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  • DOI: https://doi.org/10.1134/S0081543808040056

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