About the reliability of nonbranching programs in the basis of a generalized conjunction

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.