On the reliability of non-branching programs with an unreliable conditional stopping operator in an arbitrary complete finite basis

The article considers a problem of nobranching programs synthesis with a conditional stop-operator in any full finite base. In operative condition the stop-operator stops the program flow in case a unit arrives on its input. All functional operators and stop-operators are supposed to be unreliable and pass in failure conditions independently from each other. Functional operators are prone output inverse failures with probability $\epsilon (\epsilon\in(0,1/2))$. For conditional stop-operators two failure types are considered. The first type failure is characterized by the fact that the stop-operator won't work with probability $\delta (\delta\in(0,1/2))$ when a unit inflows on the stop-operator input and, hence, the program work proceeds. The second type failure is that the stop-operator will works with probability $\eta (\eta\in(0,1/2))$ when a zero inflows on the stop-operator input and, hence, the program work stops. It is proved that any Boolean function f can be realized by the nobranching program with unreliability not exceeding $max\{\epsilon,\eta\}+145\sigma^2$ for all $\epsilon\in(0,1/960]$ and $\sigma=max\{\epsilon,\delta,\eta\}$.