Resource-Bounded Complexity

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

Abstract

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]

Keywords

Polynomial Time Turing Machine Boolean Formula Kolmogorov Complexity Short Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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