List Approximation for Increasing Kolmogorov Complexity

Author Marius Zimand

Thumbnail PDF


  • Filesize: 465 kB
  • 12 pages

Document Identifiers

Author Details

Marius Zimand

Cite AsGet BibTex

Marius Zimand. List Approximation for Increasing Kolmogorov Complexity. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 58:1-58:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that on input a string x of length n returns a list with O(n^2) many strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n. We obtain similar results for other parameters, including a polynomial-time construction.
  • Kolmogorov complexity
  • list approximation
  • randomness extractor


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail