The Random Bit Model

Abstract

Chapters I–XIV are based on the premises that a perfect uniform [0,1] random variate generator is available and that real numbers can be manipulated and stored. Now we drop the first of these premises and Instead assume a perfect bit generator (i.e., a source capable of generating lid {0,1} random varlates B ₁,B ₂,…), While still assuming that real numbers can be manipulated and stored, as before: this is for example necessary when someone gives us the probabilities p _n for discrete random variate generation. The cost of an algorithm can be measured in terms of the number of bits required to generate a random variate. This model is due to Knuth and Yao (1976) who introduced a complexity theory for nonuniform random variate generation. We will report the main ideas of Knuth and Yao in this chapter.