Geodesic
About the reliability of circuits under failures of type $0$ at the outputs of elements in a complete finite basis containing some pairs of functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 10-17

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We consider the realization of Boolean functions by the circuits from unreliable elements in a complete finite basis containing some pairs of functions. 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_2020_7_a1,
     author = {M. A. Alekhina and T. A. Shornikova},
     title = {About the reliability of circuits under failures of type $0$ at the outputs of elements in a complete finite basis containing some pairs of functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--17},
     publisher = {mathdoc},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_7_a1/}
}
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M. A. Alekhina; T. A. Shornikova. About the reliability of circuits under failures of type $0$ at the outputs of elements in a complete finite basis containing some pairs of functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 10-17. http://geodesic.mathdoc.fr/item/IVM_2020_7_a1/