Kolmogorov entropy in the context of computability theory

  • Authors:
  • Andrej A. Muchnik;Semen Ye. Positselsky

  • Affiliations:
  • Institute of New Technologies of Education (INT), Moscow, Russia;Institute of New Technologies of Education (INT), Moscow, Russia

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

We consider the overgraph of the Kolmogorov entropy function and study whether it is a complete enumerable set with respect to different types of reductions. It turns out that (for any type of entropy) the overgraph of the conditional entropy function is m-.