Descriptive Complexity of Computable Sequences

  • Bruno Durand
  • Alexander Shen
  • Nikolai Vereshagin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)


Our goal is to study the complexity of infinite binary recursive sequences. We introduce several measures of the quantity of information they contain. Some measures are based on size of programs that generate the sequence, the others are based on the Kolmogorov complexity of its finite prefixes. The relations between these complexity measures are established. The most surprising among them are obtained using a specific two-players game.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Bruno Durand
    • 1
  • Alexander Shen
    • 2
  • Nikolai Vereshagin
    • 3
  1. 1.LIP, Ecole Normale Supérieure de LyonLyon Cedex 07France
  2. 2.Institute of Problems of Information TransmissionMoscowRussia
  3. 3.Dept. of Mathematical Logic and Theory of AlgorithmsMoscow State UniversityVorobjevy Gory, MoscowRussia

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