Comparison between the complexity of a function and the complexity of its graph

  • Bruno Durand
  • Sylvain Porrot
Contributed Papers Picture Languages - Function Systems/Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


This paper investigates in terms of Kolmogorov complexity the differences between the information necessary to compute a recursive function and the information contained in its graph. Our first result is that the complexity of the initial parts of the graph of a recursive function, although bounded, has almost never a limit. The second result is that the complexity of these initial parts approximate the complexity of the function itself in most cases (and in the average) but not always.


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  1. [1]
    C. Calude. Information and Randomness, an Algorithmic Perspective. Springer-Verlag, 1994.Google Scholar
  2. [2]
    B. Durand, Alexander Shen, and Nikolai Vereshchagin. Descriptive complexity of computable sequences. Draft, 1998.Google Scholar
  3. [3]
    M. Li and P. Vitányi. An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag, 2 edition, 1997.Google Scholar
  4. [4]
    D. W. Loveland. A variant of the Kolmogorov concept of complexity. Information and Control, 15:510–526, 1969.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    S. Porrot, M. Dauchet, B. Durand, and N. Vereshchagin. Deterministic rational transducers and random sequences. In FOSSACS'98, volume 1378 of Lecture Notes in Computer Science, pages 258–272. Springer-Verlag, march 1998.Google Scholar
  6. [6]
    V. A. Uspensky and A. Shen. Relations between varieties of Kolmogorov complexities. Math. Syst. Theory, 29(3):270–291, 1996.MathSciNetGoogle Scholar
  7. [7]
    A.K. Zvonkin and L.A. Levin. The complexity of finite objects and the development of the concepts of information and randomness by means of theory of algorithms. Russian Math. Surveys, 25(6):83–124, 1970.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bruno Durand
    • 1
  • Sylvain Porrot
    • 2
  1. 1.LIP, ENS-Lyon CNRSLyon Cedex 07France
  2. 2.LAIL and LIFLUniversité des Sciences et Technologies de LilleVilleneuve d'Ascq CedexFrance

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