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Elements of information theory
Elements of information theory
Interval algorithm for random number generation
IEEE Transactions on Information Theory
Entropy of the induced transformations associated with the interval algorithm
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
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We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.