The influence of the data presentation on the computational power of machines

  • Rutger Verbeek
  • Klaus Weihrauch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 45)


The influence of the data presentation on the computational complexity of functions is studied from a general point of view. The main emphasis lies on transformations Tυ induced by bijective changes ν of the presentation. Several sufficient conditions are given for very complex functions f such that Tυ−1 (f) is simple for an appropriate ν. On the other hand there are intrinsicially difficult functions that cannot be transformed into simple functions by any Tυ. Usually several functions shall be transformed simultaneously into simple functions. The following result gives a strong limitation of the power of data change: If Tυ is such that any primitive recursive (p.r.) f remains p.r., then no not p.r. function can be transformed into a p.r. function.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Rutger Verbeek
    • 1
    • 2
  • Klaus Weihrauch
    • 1
    • 2
  1. 1.Institut für InformatikUniversität BonnGermany
  2. 2.Informatik IBonnW-Germany

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