Abstract:
We consider the realization of Boolean functions by circuits from unreliable functional gates in full finite basis. We assume that each gate of the circuit is exposed to arbitrarily faults, and the gates faults are statistically independent. We construct the circuits for all Boolean functions and get their upper bound of the unreliability which depends on the worst (the most unreliable) of the basic gate.
Keywords:
unreliable functional gates, reliability and unreliability of circuit, synthesis of circuits composed of unreliable gates.
Citation:
M. A. Alekhina, Yu. S. Gusynina, T. A. Shornikova, “Upper estimate of unreliability of schemes in full finite basis (in P2) for arbitrary faults of gates”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 12, 80–83; Russian Math. (Iz. VUZ), 61:12 (2017), 70–72
\Bibitem{AleGusSho17}
\by M.~A.~Alekhina, Yu.~S.~Gusynina, T.~A.~Shornikova
\paper Upper estimate of unreliability of schemes in full finite basis (in $P_2$) for arbitrary faults of gates
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 12
\pages 80--83
\mathnet{http://mi.mathnet.ru/ivm9311}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 12
\pages 70--72
\crossref{https://doi.org/10.3103/S1066369X17120088}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85037047043}
Linking options:
https://www.mathnet.ru/eng/ivm9311
https://www.mathnet.ru/eng/ivm/y2017/i12/p80
This publication is cited in the following 8 articles:
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”, Russian Math. (Iz. VUZ), 64:7 (2020), 7–12
S. M. Grabovskaya, M. A. Alekhina, “O skol ugodno nadezhnoi realizatsii bulevykh funktsii nevetvyaschimisya programmami s operatorom uslovnoi ostanovki v bazisakh s obobschennoi kon'yunktsiei”, PDM, 2019, no. 43, 70–77
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”, Russian Math. (Iz. VUZ), 63:6 (2019), 79–81
M. A. Alekhina, S. M. Grabovskaya, Yu. S. Gusynina, “Dostatochnye usloviya realizatsii bulevykh funktsii asimptoticheski optimalnymi po nadezhnosti skhemami s trivialnoi otsenkoi nenadezhnosti pri neispravnostyakh tipa 0 na vykhodakh elementov”, PDM, 2019, no. 45, 44–54
M. Alekhina, O. Barsukova, T. Shornikova, “About the reliability of circuits in the complete finite basis containing an essential linear function”, Lobachevskii J. Math., 40:12 (2019), 2027–2033
M. A. Alekhina, “O nadezhnosti skhem pri neispravnostyakh tipa 0 na vykhodakh elementov v polnom konechnom bazise, soderzhaschem lineinuyu funktsiyu dvukh peremennykh i obobschennuyu diz'yunktsiyu”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2019, no. 1, 56–62
S. M. Grabovskaya, “O nadezhnosti nevetvyaschikhsya programm v bazise, soderzhaschem shtrikh Sheffera”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2018, no. 4, 33–38
S. M. Grabovskaya, “O nadezhnosti nevetvyaschikhsya programm v bazise, soderzhaschem obobschennuyu kon'yunktsiyu, pri proizvolnykh neispravnostyakh vychislitelnykh operatorov”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2017, no. 3, 28–36
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