Geodesic
Reliability of nonbranching programs in an arbitrary complete finite basis
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 13-22

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We consider the realization of Boolean functions by nonbranching programs with conditional stop-operators in an arbitrary complete finite basis. We assume that conditional stop-operators are absolutely reliable, while all functional operators are prone to output inverse failures independently of each other with probability $\varepsilon$ from the interval (0,1/2). We prove that any Boolean function is realizable by a nonbranching program with unreliability $\varepsilon+81\varepsilon^2$ for all $\varepsilon\in(0,1/960]$.
Keywords: Boolean functions, nonbranching programs, conditional stop-operator, synthesis, reliability. 
@article{IVM_2012_2_a1,
     author = {M. A. Alekhina and S. M. Grabovskaya},
     title = {Reliability of nonbranching programs in an arbitrary complete finite basis},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {13--22},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_2_a1/}
}
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M. A. Alekhina; S. M. Grabovskaya. Reliability of nonbranching programs in an arbitrary complete finite basis. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 13-22. http://geodesic.mathdoc.fr/item/IVM_2012_2_a1/