Geodesic
The reliability of circuits in the basis of unreliable and absolutely reliable gates
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 111-112 Cet article a éte moissonné depuis la source Math-Net.Ru

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The implementation of Boolean functions by circuits in the standard basis containing conjunction, disjunction and inversion is considered. It is assumed that some of the basic gates (e.g. conjunctor) are reliable, and the rest (inverter, disjunctor) are unreliable, i.e., with a probability $\varepsilon\in(0,1/2)$, they are subjected to inverse faults at the outputs. It is also assumed that all unreliable circuit gates get faulty independently of each other. Some answers to the following questions are obtained: what is the unreliability of a circuit, if some of the basic elements are reliable, while others are unreliable?
Keywords: absolutely reliable and unreliable functional gates, reliability of circuits, unreliability of circuits, inverse failures on outputs of gates. 
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M. A. Alekhina; A. E. Lakomkina. The reliability of circuits in the basis of unreliable and absolutely reliable gates. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 111-112. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a47/

[1] Von Neuman J., “Probabilistic logics and the synthesis of reliable organisms from unreliable components”, Automata Studies, eds. C. Shannon, J. McCarthy, Princeton University Press, Princeton, NJ, 1956, 329–378 ; Avtomaty, IL, M., 68–139 | MR

[2] Yablonskii S. V., “Asimptoticheski nailuchshii metod sinteza nadezhnykh skhem iz nenadezhnykh elementov”, Banach Center, 7, 1982, 11–19 | MR

[3] Vasin A. V., “Ob asimptoticheski optimalnykh skhemakh v bazise $\{x\,x\vee y,\bar x\}$ pri inversnykh neispravnostyakh na vykhodakh elementov”, Izv. vuzov. Povolzhskii region. Fiziko-matematicheskie nauki, 2008, no. 4, 3–17