  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.
