This technique is applied to establish a generic lower bound on the size of randomized OBDDs with bounded error for the so-called “k-stable” functions which have been studied in the literature on read-once branching programs and OBDDs for a long time. It follows by our result that several standard functions are not contained in the analog of the class BPP for OBDDs.

It is well-known that k-stable functions are hard for deterministic read-once branching programs. Nevertheless, there is no generic lower bound on the size of randomized read-once branching programs for these functions as for OBDDs. This is proven by presenting a randomized read-once branching program of polynomial size, even with zero error, for a certain k-stable function. As a consequence, we obtain that P _≠ ^⊂ ZPP ∩ NP ∩ coNP for the analogs of these classes defined in terms of the size of read-once branching programs.