A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Classification of computable functions by primitive recursive classes
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
On the size of programs in subrecursive formalisms
STOC '70 Proceedings of the second annual ACM symposium on Theory of computing
Classes of computable functions defined by bounds on computation: Preliminary Report
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
The complexity of loop programs
ACM '67 Proceedings of the 1967 22nd national conference
On the structure of subrecursive degrees
Journal of Computer and System Sciences
On the density of honest subrecursive classes
Journal of Computer and System Sciences
Polynomial and abstract subrecursive classes
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Degrees of total algorithms versus degrees of honest functions
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
| Hi-index | 0.00 |
A classification of all the computable functions is given in terms of subrecursive programming languages. These classes are those which arise from the relation ''primitive recursive in''. By distinguishing between honest and dishonest classes the classification is related to the computational complexity of the functions classified and the classification has a wide degree of measure invariance. The structure of the honest and dishonest classes under inclusion is explored. It is shown that any countable partial ordering can be embedded in the dishonest classes, and that the dishonest classes are dense in the honest classes. Every honest class is minimal over some dishonest class, but there are dishonest classes with no honest class minimal over them.