The talk will present several general results on the testing of the RNG's based on the theory of the dynamical systems with discrete phase space, the limit theorems for the quantum statistics and the recent ideas by Kalman, Pirckus and Singer on the computational enthropy and comlexity. The corresponding tests were applied to the classical RNG's as well to some physical generators ( including prototype RNG using "alpha"-particles decay). We will discuss the statistical results of testing.