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The complexity of depth-two information networks

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Abstract

The lower bound Ω(n log2 n) for the complexity of an arbitrary depth-two information network with n inputs and n outputs is proved providing the inputs are independent, the outputs are independent, and the total information of any input and any output is n times less than the entropy of any input or output. A similar estimate for Boolean depth-two circuits of functional elements is obtained as a corollary.

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    D. Yu. Cherukhin

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  1. D. Yu. Cherukhin
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Original Russian Text © D.Yu.Cherukhin, 2009, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2009, Vol. 64, No. 1, pp. 16–19.

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Cherukhin, D.Y. The complexity of depth-two information networks. Moscow Univ. Math. Bull. 64, 16–19 (2009). https://doi.org/10.3103/S0027132209010045

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  • DOI: https://doi.org/10.3103/S0027132209010045

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