Abstract
We elicit the necessary and sufficient conditions under which an unreliable functional element with two binary inputs and one binary output is a Sheffer element, i.e., permits us to construct circuits realizing arbitrary functions of the algebra of logic with arbitrarily high reliability.
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J. von Neumann, “Probabilistic logic and the synthesis of reliable organisms from unreliable components,” in: Automata Studies, C. E. Shannon and J. McCarthy (editors), Princeton Univ. Press, Princeton, N. J. (1954).
S. G. Gindikin and A. A. Muchnik, “Solution of the completeness problem for systems of functions of logical algebra with an unreliable realization,” in: Problems of Cybernetics, Vol. 15 [in Russian], Fizmatgiz, Moscow (1965), pp. 65–85.
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V. V. Tarasov, “On the completeness problem for systems of functions of logical algebra with an unreliable realization,” Mat. Sb.,98, No. 3, 378–394 (1975).
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Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 391–400, September, 1976.
The author thanks S. V. Yablonskii for posing the problem and for valuable advice.
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Tarasov, V.V. The synthesis of reliable circuits from unreliable elements. Mathematical Notes of the Academy of Sciences of the USSR 20, 775–780 (1976). https://doi.org/10.1007/BF01097249
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DOI: https://doi.org/10.1007/BF01097249