Random number generation using a biased source.

摘要

We study random number generation using a biased source motivated by previous works on this topic, mainly, von Neumman (1951), Elias (1972), Knuth and Yao (1976) and Peres (1992). We study the problem in two cases: first, when the source distribution is unknown, and second, when the source distribution is known. In the first case, we characterize the functions that use a discrete random source of unknown distribution to simulate a target discrete random variable with a given rational distribution. We identify the functions that minimize the ratio of source inputs to target outputs. We show that these optimal functions are efficiently computable. In the second case, we prove that it is impossible to construct an optimal tree algorithm recursively, using algebraic decision procedures. Our model of computation is sufficiently general to encompass previously known algorithms for this problem.