Lower estimation of unreliability of non-branching programs with conditional stop operator

The article considers a problem of synthesis of nobranching programs with conditional stop-operator. All functional operators are supposed to be subject to output inverse failures with probability $\epsilon (\epsilon \in (0,1/2))$. Conditional stop-operators are absolutely reliable. Any boolean function $f \in K$ (class $K$ is found explicitly) is proved to be impossible to realize by irreducible nobranching program with unreliability of less than $\epsilon (1 - \epsilon)^m$, where $m$ - the number of functional operators in the program. These and the previous results on the upper bound for the unreliability of the nobranching programs prove that almost all functions can be realized by asymptotically optimal reliable nobranching programs that operate with unreliability asymptotically equal to $\epsilon$ at $\epsilon \to 0$.