Non-reducible descriptions for conditional kolmogorov complexity

  • Authors:

  • Andrej Muchnik;Alexander Shen;Nikolai Vereshchagin;Michael Vyugin

  • Affiliations:

  • Institute of New Technologies;LIF CNRS, Marseille, France;Moscow State University;Moscow State University

  • Venue:
  • TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let a program p on input a outputs b. We are looking for a shorter program p′ having the same property (p′(a)=b). In addition, we want p′ to be simple conditional to p (this means that the conditional Kolmogorov complexity K (p′|p) is negligible). In the present paper, we prove that sometimes there is no such program p′, even in the case when the complexity of p is much bigger than K (b|a). We give three different constructions that use the game approach, probabilistic arguments and algebraic (combinatorial) arguments, respectively.