Problems of the effective synthesis of fastest programs (modulo a recursive factor) for recursive functions given by input-output examples or an arbitrary program are investigated. In spite of the negative result proved by AL/TON we point out that even for function classes containing arbitrarily complex functions sometimes the effective synthesis of fastest programs (modulo a recursive factor) can be achieved.


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  1. [1]
    Alton, D.A., Non-existence of Program Optimizers in Several Abstract settings. J. Comp. System Sci. 12, 1976, 368–393Google Scholar
  2. [2]
    Blum, M., Machine Independent Theory of Complexity of Recursive Functions. J. ACM 14, 1967, 322–336Google Scholar
  3. [3]
    Blum, L. and M. Blum, Toward a Mathematical Theory Of Inductive Inference. Inf. and Control 28, 1975, 122–155Google Scholar
  4. [4]
    Freivalds, R., Private CommunicationGoogle Scholar
  5. [5]
    Helm, J., P., On Effectively Computable Operators. ZML 17, 1971, 231–244Google Scholar
  6. [6]
    Lindner, R., Algorithmische Erkennung. Diss. B, Jena 1972Google Scholar
  7. [7]
    Lowther, J., L., The Non-existence of Optimizers and Subrecursive Languages. Dept. of Comp. Sci., The University of Iowa, Iowa City, Technical Report 75–07, 1975Google Scholar
  8. [8]
    Rogers, H., Jr., Theory of Recursive Functions and Effictive Computability. Mc Graw-Hill, New York 1967Google Scholar
  9. [9]
    Trachtenbrot, B., A. and J.M. Barzdin, Finite Automata-behavior and synthesis. Nauka, Moskau 1970 (in russian) or Fundamental studies in Comp. Sci. 1, North Holland/American Elsevier 1973 (in english)Google Scholar
  10. [10]
    Zeugmann, T., A-posteriori Characterizations in Inductive Inference of Recursive Functions. EIK 19, 1983, 559–594Google Scholar
  11. [11]
    Zeugmann, T., On the Synthesis of Fastest Programs in Inductive Inference. EIK 19, 1983, 625–642Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Thomas Zeugmann
    • 1
  1. 1.Sektion Mathematik der Humboldt-Universität zu BerlinBerlinGerman Democratic Republic

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