On the complexity of binary floating point pseudorandom generation

Abstract

AbstractThe paper is devoted to the complexity analysis of binary floating point pseudorandom generators. We start with a stochastic model of a “usual” pseudorandom generator (PRNG). Then integer outputs of this generator are transformed into i.i.d. random variables, agreed with an abstract binary floating point system. Additionally, these random variables are approximately uniformly distributed on the interval [0,1]. Therefore, they can interpreted as (random) outputs of a binary floating point pseudorandom generator (flPRNG). The simulation complexity of such a transformation is defined as the average number of PRNG's outputs necessary to produce the unique output of flPRNG. Several transformations with minimal or approximately minimal complexities are presented and discussed.