On reliability of circuits over an arbitrary complete finite basis under single-type constant faults at outputs of elements. (English. Russian original) Zbl 1262.94028
Discrete Math. Appl. 22, No. 4, 383-391 (2012); translation from Diskretn. Mat. 24, No. 3, 17-24 (2012).
Summary: We consider the realisation of Boolean functions by circuits with unreliable functional elements over an arbitrary complete finite basis \(B\). It is assumed that all elements of the circuit are subject to single-type constant faults at the outputs which are independent of each other and occur with probability \(\gamma\), \(\gamma\in (0,1/2)\).
It is proved that all Boolean functions over the basis \(B\) can be realised by circuits with unreliability no greater than \(3\gamma + 27\gamma^2\) for all \(\gamma\in (0,1/960)\).
It is proved that all Boolean functions over the basis \(B\) can be realised by circuits with unreliability no greater than \(3\gamma + 27\gamma^2\) for all \(\gamma\in (0,1/960)\).
MSC:
| 94C10 | Switching theory, application of Boolean algebra; Boolean functions (MSC2010) |
| 94C12 | Fault detection; testing in circuits and networks |
