  Currently, statistical tests for random number generators (RNGs) are widely
used in practice, and some of them are even included in information security
standards. But despite the popularity of RNGs, consistent tests are known only
for stationary ergodic deviations of randomness (a test is consistent if it
detects any deviations from a given class when the sample size goes to $ \infty
$). However, the model of a stationary ergodic source is too narrow for some
RNGs, in particular, for generators based on physical effects. In this article,
we propose computable consistent tests for some classes of deviations more
general than stationary ergodic and describe some general properties of
statistical tests. The proposed approach and the resulting test are based on
the ideas and methods of information theory.
