Geodesic
About the reliability of nonbranching programs in the basis of a~generalized conjunction
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 1, pp. 33-40.

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The problem of synthesis of nonbranching programs with conditional stop-operator is considered in a full finite basis which contains functions of the form $x_1\cdot x_2$, $\overline x_1\cdot x_2$ or $\overline x_1\cdot\overline x_2$. All functional operators are supposed to be prone to output inverse failures with probability $\varepsilon\in(0,1/2)$ and conditional stop-operators are absolutely reliable. Any Boolean function is proved to be realized by a nonbranching program with unreliability no more then $\varepsilon+59\varepsilon^2$ at $\varepsilon\in(0,1/960]$. Ill. 1, bibliogr. 4.
Keywords: Boolean function, nonbranching program, conditional stop-operator, synthesis, reliability. 
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S. M. Grabovskaya. About the reliability of nonbranching programs in the basis of a~generalized conjunction. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 1, pp. 33-40. http://geodesic.mathdoc.fr/item/DA_2012_19_1_a2/

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