Random Sets in Subrecursive Hierarchies

Abstract

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. © 1969, ACM. All rights reserved.