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Improvement of Nonmonotone Complexity Estimates of \(k\)-Valued Logic Functions

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Abstract

The problem of determining the nonmonotone complexity of the implementation of \(k\)-valued logic functions by logic circuits in bases consisting of all monotone (with respect to the standard order) functions and finitely many nonmonotone functions is investigated. In calculating the complexity measure under examination only those elements of the circuit which are assigned nonmonotone basis functions are taken into account. The nonmonotone complexity of an arbitrary \(k\)-valued logic function is determined with high accuracy, namely, upper and lower bounds which differ by a constant not exceeding \(3 \log_2 k+4\) are found.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of a program of the Moscow Center for Fundamental and Applied Mathematics (contract no. 075-15-2022-284).

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. V. Kochergin

  2. National Research University Higher School of Economics, Moscow, 101978, Russia

    V. V. Kochergin & A. V. Mikhailovich

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    V. V. Kochergin & A. V. Mikhailovich

Authors
  1. V. V. Kochergin
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  2. A. V. Mikhailovich
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Correspondence to V. V. Kochergin.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 849–862 https://doi.org/10.4213/mzm13759.

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Kochergin, V.V., Mikhailovich, A.V. Improvement of Nonmonotone Complexity Estimates of \(k\)-Valued Logic Functions. Math Notes 113, 794–803 (2023). https://doi.org/10.1134/S0001434623050218

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  • DOI: https://doi.org/10.1134/S0001434623050218

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