Resource-Bounded Complexity

  • Ming Li
  • Paul Vitányi
Part of the Texts and Monographs in Computer Science book series (MCS)


Recursion theory has a resource-bounded version in computational complexity theory. Similarly, Kolmogorov complexity has resource-bounded Kolmogorov complexity (also known as generalized Kolmogorov complexity). Several authors suggested early on the possibility of restricting the power of the device used to compress strings. Says Kolmogorov:

“The concept discussed ... does not allow for the ‘difficulty’ of preparing a program p for passing from an object x to an object y. ... [some] object permitting a very simple program, i.e., with very small complexity K(x) can be restored by short programs only as the result of computations of a thoroughly unreal nature. ... [this concerns] the relationship between the necessary complexity of a program and its permissible difficulty t. The complexity K(x) that was obtained [before] is, in this case, the minimum of K t (x) on the removal of the constraints on t.” [Kolmogorov]


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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Ming Li
    • 1
  • Paul Vitányi
    • 2
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands

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