Chapter 10: Processes of Perception and Analysis

Section 9: Statistical Analysis

Randomized algorithms

Whether a randomized algorithm gives correct answers can be viewed as a test of randomness for whatever supposedly random sequence is provided to it. But in most practical cases such tests are not particularly stringent; linear congruential generators, for example, almost always pass. (There are perhaps exceptions in VLSI testing.) And this is basically why it has so often proved possible to replace randomized algorithms by deterministic ones that are at least as efficient (see page 1192). An example is Monte Carlo integration, where what ultimately matters is uniform sampling of the integrand—which can usually be achieved better by quasi-random irrational number multiple (see page 903) or digit reversal (see page 905) sequences than by sequences one might consider more random.

From Stephen Wolfram: A New Kind of Science [citation]