A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
An Overview of the Theory of Computational Complexity
Journal of the ACM (JACM)
Classes of computable functions defined by bounds on computation: Preliminary Report
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
Dense and non-dense families of complexity classes
SWAT '69 Proceedings of the 10th Annual Symposium on Switching and Automata Theory (swat 1969)
Journal of Computer and System Sciences
Applied Ontology
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We consider a measure @F of computational complexity. The measure @F determinesa binary relation on the recursive functions; F is no harder to compute than G iff for every index g of G there is an index f of F such that for nearly all x, the difficulty of f at x (as measured by @F) is no more than the difficulty of g at x. The corresponding symmetric relation is an equivalence relation, and the set of equivalence classes (the degrees of complexity) is partially ordered. In this paper we give a simple proof of a result of McCreight: An arbitrary countable partial ordering can be embedded in this ordering of degrees of complexity.