Classes of computable functions defined by bounds on computation: Preliminary Report

  • Authors:

  • E. M. McCreight;A. R. Meyer

  • Affiliations:

  • Department of Computer Science, Carnegie-Mellon University, Pittsburgh, Pa;Department of Computer Science, Carnegie-Mellon University, Pittsburgh, Pa

  • Venue:
  • STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
  • Year:
  • 1969

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Abstract

The structure of the functions computable in time or space bounded by t is investigated for recursive functions t. The t-computable classes are shown to be closed under increasing recursively enumerable unions; as a corollary the primitive recursive functions are shown to equal the t-computable functions for a certain recursive t. Any countable partial order can be isomorphically embedded in the family of t-computable classes partially ordered by set inclusion. For any recursive t, there is a recursive t' which is (approximately) equal to an actual running time such that the t-computable functions equal the t'-computable functions.