Evaluation of splittable pseudo-random generators

Pseudo-random number generation is a fundamental problem in computer Programming. In the case of sequential Processing the problem is very well researched, but parallel Processing raises New problems whereof far too little is currently understood. Splittable pseudo-randomgenerators (S-PRNG) have been proposed to meet the Challenges of parallelism. While applicable to any Programming paradigm, they are designed to be particularly suitable for pure functional Programming. In this paper, we review and evaluate known Constructions of such generators, and we identify flaws in several large classes of generators, including Lehmer trees, the implementation in Haskell's standard Library, leapfrog, and subsequencing (substreaming).