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Asymptotic Bounds of the Shannon Function for a Depth Model of Functional-Element Networks with Capacity Parameters for Element Outputs

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The article proposes a synthesis method for amplifying networks of functional elements (ANFE) that establishes the asymptotic behavior of the Shannon function for the ANFE generalized depth, i.e., the depth of the “worst” Boolean function of n given variables, in a special basis (the depth model) where the element depth is determined both by its type and by its fan-out in the network. The asymptotic behavior of the Shannon function is established apart from a term logarithmic in n.

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References

  1. B. R. Danilov, “Asymptotic bounds of the Shannon function in a depth model for networks of functional elements with capacity parameters of element outputs,” in: Proc. X Int. Conf. on Discrete Models in Control System Theory (Moscow and Near-Moscow, 23–25 May 2018) [in Russian], MAKS Press, Moscow (2018), pp. 112–113.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    B. R. Danilov & S. A. Lozhkin

Authors
  1. B. R. Danilov
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  2. S. A. Lozhkin
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Correspondence to B. R. Danilov.

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Translated from Prikladnaya Matematika i Informatika, No. 59, 2018, pp. 40–49.

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Danilov, B.R., Lozhkin, S.A. Asymptotic Bounds of the Shannon Function for a Depth Model of Functional-Element Networks with Capacity Parameters for Element Outputs. Comput Math Model 30, 129–136 (2019). https://doi.org/10.1007/s10598-019-09441-2

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  • DOI: https://doi.org/10.1007/s10598-019-09441-2

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