Geodesic
The reliability of circuits in Rosser--Turkett basis (in $P_3$) with faults of type~$0$ at the outputs of gates
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 124-126

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We consider the realization of ternary logic functions by circuits from unreliable functional elements in Rosser–Turkett basis. We assume that all circuit elements are exposed to faults of type $0$ at the outputs and they pass to fault states independently with probability $\varepsilon$ ($\varepsilon1/2$). We have obtained the following results: 1) any function of ternary logic can be realized by a circuit with unreliability that is asymptotically not more than $\varepsilon$ for small $\varepsilon$; 2) for any function except the constant $0$ and the variable $ x_i$ ($i\in\mathbb N$), such a circuit is asymptotically optimal to reliability and operates with the unreliability asymptotically equalled $\varepsilon$ for small $\varepsilon$; 3) the functions $0$ and $x_i $ can be realized absolutely reliably.
Keywords: ternary logic functions, circuit from functional gates, unreliability of a circuit, reliability of a circuit, faults of type $0$. 
@article{PDMA_2017_10_a47,
     author = {M. A. Alekhina and O. Yu. Barsukova},
     title = {The reliability of circuits in {Rosser--Turkett} basis  (in $P_3$) with faults of type~$0$ at the outputs of gates},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {124--126},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a47/}
}
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M. A. Alekhina; O. Yu. Barsukova. The reliability of circuits in Rosser--Turkett basis  (in $P_3$) with faults of type~$0$ at the outputs of gates. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 124-126. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a47/