A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
On classes of computable functions
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Augmented loop languages and classes of computable functions
Journal of Computer and System Sciences
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Subrecursive degrees are partitions of computable (recursive) functions generated by strong reducibility orderings. Such reducibilities can be naturally characterized in terms of closure operations. Closure operations corresponding to standard reducibilities such as ''primitive recursive,'' etc., are computation time closed. It is shown that if the closure operation defining a strong reducibility satisfies certain axioms, then the partial ordering of the subrecursive degrees contains dense chains.