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. 
@article{IVM_2016_7_a0,
     author = {M. A. Alekhina and V. V. Kurysheva},
     title = {On reliability of circuits in a~basis ``anticonjunction'' with constant faults at the input gates},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_7_a0/}
}
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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/