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Matematicheskie Zametki, 2024, Volume 115, Issue 1, Pages 91–107
DOI: https://doi.org/10.4213/mzm14026 (Mi mzm14026) 		 
Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates

K. A. Popkov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/mzm14026
Abstract: We prove that if a Boolean function essentially depends on at least two variables, then it cannot be implemented by a circuit that consists of unreliable gates with at most two inputs each and is self-correcting with respect to at least some faults of an arbitrary number of gates. In view of the previous results, it suffices to establish this fact for linear functions.
Keywords: logic circuit, self-correction, unreliable gate, linear Boolean function.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-283
This work was supported by the Moscow Center for Fundamental and Applied Mathematics (contract with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-283).
Received: 11.05.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 1, Pages 77–88
DOI: https://doi.org/10.1134/S0001434624010073
Bibliographic databases:
Document Type: Article
UDC: 519.718.42
MSC: 94C12
Language: Russian
Citation: K. A. Popkov, “Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates”, Mat. Zametki, 115:1 (2024), 91–107; Math. Notes, 115:1 (2024), 77–88
Citation in format AMSBIB
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\by K.~A.~Popkov
\paper Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates
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\pages 91--107
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\crossref{https://doi.org/10.4213/mzm14026}
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\transl
\jour Math. Notes
\yr 2024
\vol 115
\issue 1
\pages 77--88
\crossref{https://doi.org/10.1134/S0001434624010073}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85190880923}
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