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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical Backgrounds of Computer and Control System Reliability
Asymptotically optimal in unreliability circuits in the basis consisting of the Webb function in $P_3$ under faults of type $2$ at the outputs of elements
O. Yu. Barsukovaa, M. A. Alekhinab a Penza State University, Penza, Russia
b Penza State Technological University, Penza, Russia
Abstract:
We consider the realization of ternary logic functions by circuits from unreliable elements in full basis consisting of the Webb function. We assume that elements of the circuit pass to fault states independently of each other, and they are exposed to single-type constant faults of type $2$ at the outputs. It is proved that any function of ternary logic can be realized by an asymptotically optimal in reliability circuit functioning with unreliability which is asymptotically no more $3\varepsilon$ with $\varepsilon\rightarrow 0$. A class of functions is found (it contains almost all ternary logic functions), each of which cannot be implemented by a circuit whose unreliability is asymptotically less $3\varepsilon$ with $\varepsilon\rightarrow 0$. Thus, it is proved that almost any function of ternary logic can be implemented by an asymptotically optimal on reliability circuit operating with unreliability which is asymptotically equal to $3\varepsilon$ with $\varepsilon\rightarrow 0$.
Keywords:
ternary logic functions, unreliable functional elements, reliability and unreliability of circuit, synthesis of circuits from unreliable elements, faults at outputs of elements.
Citation:
O. Yu. Barsukova, M. A. Alekhina, “Asymptotically optimal in unreliability circuits in the basis consisting of the Webb function in $P_3$ under faults of type $2$ at the outputs of elements”, Prikl. Diskr. Mat., 2020, no. 47, 22–29
Linking options:
https://www.mathnet.ru/eng/pdm692 https://www.mathnet.ru/eng/pdm/y2020/i1/p22
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Abstract page: | 152 | Full-text PDF : | 42 | References: | 29 |
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