Loop programs and classes of primitive recursive functions

  • Bernhard Goetze
  • Werner Nehrlich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 64)


A refinement of the structural complexity measure depth of nesting in loop programs leads to a new characterization of Cleave's ω2-hierarchy. This characterization allows to discover new properties (for instance Universal Function Theorem) or to reproduce already known properties of this hierarchy. A further refinement leads to a natural definition of a (ωω)-hierarchy, whose properties resemble those of Cleave's hierarchy.


Turing Machine Recursive Function Natural Definition Loop Program Universal Turing Machine 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Bernhard Goetze
    • 1
  • Werner Nehrlich
    • 1
  1. 1.Sektion MathematikFriedrich-Schiller-Universität JenaJenaGDR

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