On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
On the Effective Definition of Random Sequence
On the Effective Definition of Random Sequence
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Successive modifications of Church's definition of a random sequence are considered in terms of their relative position in the Ritchie hierarchy of Kalmar elementary functions. A general result is derived governing the classification of Church random sequences in subrecursive hierarchies which include the elementary functions, such as the Grzegorczyk and Kleene subrecursive hierarchies.