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About Reliability of Circuits with Faults of Type 0 at the Outputs of Elements in a Full Finite Basis Containing a Special Function

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Abstract

We consider a realization of Boolean functions by the circuits from unreliable elements in a full basis B, containing a special function. We assume that all elements of a circuit are exposed to the faults type 0 at the outputs with probability ε ∈ (0, 1/2) independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to ε with ε → 0.

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References

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Funding

This research is supported by the Russian Foundation for Basic Research (project no. 17-01-00451a).

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Authors and Affiliations

  1. Penza State Technological University, 1a/1 Baidukova pas. / Gagarina str., Penza, 440039, Russia

    M. A. Alekhina, Yu. S. Gusynina & T. A. Shornikova

Authors
  1. M. A. Alekhina
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  2. Yu. S. Gusynina
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  3. T. A. Shornikova
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Corresponding authors

Correspondence to M. A. Alekhina, Yu. S. Gusynina or T. A. Shornikova.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 6, pp. 85–88.

Submitted by I. V. Konnov

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Alekhina, M.A., Gusynina, Y.S. & Shornikova, T.A. About Reliability of Circuits with Faults of Type 0 at the Outputs of Elements in a Full Finite Basis Containing a Special Function. Russ Math. 63, 79–81 (2019). https://doi.org/10.3103/S1066369X19060094

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  • DOI: https://doi.org/10.3103/S1066369X19060094

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