On the algorithm of detecting the essential arguments of random Boolean function

Earlier author had presented the algorithm for detection of essential arguments of the binary vector-function given $N$ random uniformly distributed arguments and distorted values of the function. The dependence on $N$ of the probability that all (or almost all) essential arguments of Boolean function $f$ are detected on the first stage of the algorithm is studied. Cases of random symmetric and random threshold functions $f$ are considered. A review of some relevant papers is given.