Pseudorandom Number Generator - Problems With Deterministic Generators

Problems With Deterministic Generators

In practice, the output from many common PRNGs exhibit artifacts which cause them to fail statistical pattern detection tests. These include:

• Shorter than expected periods for some seed states (such seed states may be called 'weak' in this context);
• Lack of uniformity of distribution for large amounts of generated numbers;
• Correlation of successive values;
• Poor dimensional distribution of the output sequence;
• The distances between where certain values occur are distributed differently from those in a random sequence distribution.

Defects exhibited by flawed PRNGs range from unnoticeable (and unknown) to very obvious. An example was the RANDU random number algorithm used for decades on mainframe computers. It was seriously flawed, but its inadequacy went undetected for a very long time. In many fields, much research work of that period which relied on random selection or on Monte Carlo style simulations, or in other ways, is less reliable than it might have been as a result.