Geodesic
On reliability of circuits in a~basis ``anticonjunction'' with constant faults at the input gates
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 3-9.

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We consider the realization of Boolean functions by circuits from unreliable functional gates in the basis which contains anticonjunction, only. We assume that each gate of the circuit is exposed to the faults of type 0 at the inputs or the faults of type 1 at the inputs. We construct the circuits for all Boolean functions and get their upper bound of unreliability which depends only on the probabilities of appearance of the fault of type 0 and of the fault of type 1 at the inputs. We prove that the found upper bound of the unreliability is asymptotically (for small values of probability) exact for almost all Boolean functions.
Keywords: unreliable functional gate, circuit asymptotically optimal with respect to reliability, constant fault at the inputs of gates, synthesis of circuits composed of unreliable gates. 
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M. A. Alekhina; V. V. Kurysheva. On reliability of circuits in a~basis ``anticonjunction'' with constant faults at the input gates. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2016_7_a0/

[1] fon Neiman Dzh., Veroyatnostnaya logika i sintez nadezhnykh organizmov iz nenadezhnykh komponent, In. lit., M., 1956, 68–139

[2] Ortyukov S. I., “Ob izbytochnosti realizatsii bulevykh funktsii skhemami iz nenadezhnykh elementov”, Tr. semin. po diskretn. matem. i ee prilozh. (Moskva, 27–29 yanvarya 1987 g.), Izd-vo MGU, M., 1989, 166—168

[3] Uhlig D., “Reliable networks from unreliable gates with almost minimal comlexity”, Proc. Intern. Conf. Fundamentals of Computation Theory, FCT' 87 (Kazan, June 1987), Lect. Notes in Comput. Sci., 278, Springer-Verlag, Berlin, 1987, 462–469 | DOI

[4] Alekhina M. A., Sintez, nadezhnost i slozhnost skhem iz nenadezhnykh funktsionalnykh elementov, Diss. $\dots$ dokt. fiz.-matem. nauk, Penza, 2004

[5] Alekhina M. A., “Nizhnie otsenki nenadezhnosti skhem v nekotorykh bazisakh pri odnotipnykh konstantnykh neispravnostyakh na vkhodakh elementov”, Diskretn. analiz i issledov. operatsii. Ser. 1, 9:3, iyul–sentyabr (2002), 3–28 | MR | Zbl

[6] Alekhina M. A., “Sintez i slozhnost nadezhnykh skhem iz nenadezhnykh elementov”, Matem. voprosy kibernetiki, 11, 2002, 193–218 | MR | Zbl

[7] Alekhina M. A., “O nadezhnosti i slozhnosti skhem v bazise $\{x|y\}$ pri inversnykh neispravnostyakh na vkhodakh elementov”, Izv. vuzov. Povolzhskii region. Estestven. nauki, 2005, no. 6(21), 36–41

[8] Chugunova V. V., Sintez asimptoticheski optimalnykh po nadezhnosti skhem pri inversnykh neispravnostyakh na vkhodakh elementov, Diss. $\dots$ kand. fiz.-matem. nauk, Penza, 2007

[9] Alekhina M. A., “O nadezhnosti i slozhnosti skhem v bazise $\{x|y\}$ pri inversnykh neispravnostyakh elementov”, Diskretn. analiz i issledov. operatsii. Ser. 1, 12:2 (2005), 3–11 | MR | Zbl

[10] Alekhina M. A., Vasin A. V., “Dostatochnye usloviya realizatsii bulevykh funktsii asimptoticheski optimalnymi skhemami s nenadezhnostyu $2\varepsilon$”, Izv. vuzov. Matem., 2010, no. 5, 79–82 | MR

[11] Alekhina M. A., “Synthesis and complexity of asymptotically optimal circuits with unreliable gates”, Fundam. Inform., 104:3 (2010), 219–225 | MR | Zbl