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 a perspective of information spectral approach. When either the coin process or the target process has one point spectrum, 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. The feasibility condition of exact random number generation is also elucidated.
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