A Pseudo-Random Generator Whose Output is a Normal Sequence

Pseudo-random number generators (PRNGs) are widely used in computer simulation, cryptography, and many other fields. In this paper, we describe a PRNG class, which, firstly, has been successfully tested using the most powerful modern test batteries, and secondly, is proved to consist of generators that generate normal sequences. The latter property means that, for any generated sequence x(1)x(2) ... and any binary word w, we have lim(t ->infinity) nu t(w)/(t - vertical bar w vertical bar) = 2(-vertical bar w vertical bar), where nu(t)(w) is the number of occurrences of w in the sequence x(1) ... x(vertical bar w vertical bar), x(2) ... x(vertical bar w vertical bar+1), ..., x(t) - vertical bar w vertical bar+1 ... x(t).