# Interval Algorithm for Random Number Generation: Information Spectrum Approach

## TL;DR

This paper analyzes the interval algorithm for exact random process generation using an information spectrum approach, proving its asymptotic optimality under certain spectral conditions and illustrating its application to Markov processes.

## Contribution

It establishes the asymptotic optimality of the interval algorithm for general processes with spectral conditions and clarifies the feasibility of exact random number generation.

## Key findings

- Proves asymptotic optimality when one process has a one-point spectrum
- Provides feasibility conditions for exact random number generation
- Illustrates results with Markov process examples

## Abstract

The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the perspective of information spectrum approach. When either the coin process or the target process has one point spectrum, the asymptotic optimality of the interval algorithm among any random number generation algorithms is proved, which demonstrates utility of the interval algorithm beyond the ergodic process. Furthermore, the feasibility condition of exact random number generation is also elucidated. Finally, the obtained general results are illustrated by the case of generating a Markov process from another Markov process.