Geodesic
About the reliability of circuits with faults of type $0$ at the outputs of elements in the complete finite basis containing a special function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 85-88

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We consider a realization of Boolean functions by the circuits from unreliable elements in full basis $\mathrm{B}$, containing a special function. We assume that all elements of a circuit are exposed to the faults type $0$ at the outputs with probability $\varepsilon \in (0,1/2)$ independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to $\varepsilon$ with $\varepsilon \to 0$.
Keywords: unreliable functional gates, reliability and unreliability of circuit, synthesis of circuits composed of unreliable gates. 
@article{IVM_2019_6_a8,
     author = {M. A. Alekhina and Yu. S. Gusynina and T. A. Shornikova},
     title = {About the reliability of circuits with faults of type $0$ at the outputs of elements in the complete finite basis containing a special function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {85--88},
     publisher = {mathdoc},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_6_a8/}
}
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M. A. Alekhina; Yu. S. Gusynina; T. A. Shornikova. About the reliability of circuits with faults of type $0$ at the outputs of elements in the complete finite basis containing a special function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 85-88. http://geodesic.mathdoc.fr/item/IVM_2019_6_a8/