Geodesic
An upper bound for reliability of non-branching programs with an unreliable stop-operator
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 106-108

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A realization of Boolean functions by non-branching programs with a conditional stop-operator is considered in an arbitrary complete finite basis. All computational operators are supposed to be subject to output one-type constant faults with a probability $\varepsilon\in(0,1/2)$. Conditional stop-operators are subject to faults of two types: the first and the second kinds with probabilities $\delta\in(0,1/2)$ and $\eta\in(0,1/2)$ respectively. Three bases are considered: with a special function, with the generalized disjunction, and with the generalized conjunction. Some upper bounds for the reliability of non-branching programs in these bases are given. For an arbitrary complete finite basis, such a bound is equal to $\max\{\varepsilon,\eta\}+78\mu^2$ for each $\varepsilon\in(0,1/960]$ and $\mu=\max\{\varepsilon,\delta,\eta\}$.
Keywords: Boolean function, non-branching program, conditional stop operator, reliability, constant faults on the outputs. 
@article{PDMA_2015_8_a39,
     author = {S. M. Grabovskaya},
     title = {An upper bound for reliability of non-branching programs with an unreliable stop-operator},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {106--108},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a39/}
}
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S. M. Grabovskaya. An upper bound for reliability of non-branching programs with an unreliable stop-operator. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 106-108. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a39/