Geodesic
Lower bounds for unreliability of circuits in the Rosser--Tourkett basis
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 104-105

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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. 
@article{PDMA_2015_8_a38,
     author = {M. A. Alekhina and S. P. Kargin},
     title = {Lower bounds for unreliability of circuits in the {Rosser--Tourkett} basis},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {104--105},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     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/