Geodesic
Lower bounds for unreliability of circuits in the Rosser–Tourkett basis
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 104-105 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the implementation of four-valued logic functions by circuits consisting of unreliable functional gates in the Rosser–Tourkett basis. It is assumed that all elements of the circuit independently with probability $p$ are subject to inverse failures on the outputs, i.e. each basic element can give each of incorrect values with the probability $p$ and correct value with the probability $1-3p$. In this paper, a class $K$ of four-valued functions is introduced in such a way that almost all four-valued functions are contained in $K$ and any circuit realizing a function from $K$ operates with an unreliability that is asymptotically (for small $p$) not less than $9p$.
Keywords: four-valued logic functions, unreliable functional gates, unreliability of circuits, inverse failures on outputs of gates. 
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     author = {M. A. Alekhina and S. P. Kargin},
     title = {Lower bounds for unreliability of circuits in the {Rosser{\textendash}Tourkett} basis},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a38/}
}
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M. A. Alekhina; S. P. Kargin. Lower bounds for unreliability of circuits in the Rosser–Tourkett basis. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 104-105. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a38/

[1] Vinogradov Yu. A., “O sinteze trekhznachnykh MDP-skhem”, Matematicheskie voprosy kibernetiki, 3, Nauka, M., 1991, 187–198 | MR

[2] Vinogradov Yu. A., “O sinteze chetyrekhznachnykh kvazikomplementarnykh MOP-skhem”, Matematicheskie voprosy kibernetiki, 8, Nauka, M., 1999, 298–300

[3] Barsukova O. Yu., Sintez nadezhnykh skhem, realizuyuschikh funktsii dvuznachnoi i trekhznachnoi logik, Dis. $\dots$ kand. fiz.-mat. nauk, Penza, 2014, 87 pp.

[4] Alekhina M. A., Barsukova O. Yu., “Nenadëzhnost skhem v bazise Rossera–Turketta”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 109–110