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Complexity of the realization of a linear function in the class of II-circuits

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Abstract

It is proved that the linear function gn(x1,..., xn) = x1 + ... + xnmod 2 is realized in the class of II-circuits with complexity Lπ(gn) ≥n2. Combination of this result with S. V. Yablonskii's upper bound yields Lπ(gn)\(\begin{array}{*{20}c} \smile \\ \frown \\ \end{array}\) n2.

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Literature cited

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Authors and Affiliations

  1. Applied Mathematics Institute, Academy of Sciences of the USSR, USSR

    V. M. Khrapchenko

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  1. V. M. Khrapchenko
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Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 35–40, January, 1971.

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Khrapchenko, V.M. Complexity of the realization of a linear function in the class of II-circuits. Mathematical Notes of the Academy of Sciences of the USSR 9, 21–23 (1971). https://doi.org/10.1007/BF01405045

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  • DOI: https://doi.org/10.1007/BF01405045

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