Logical operations and Kolmogorov complexity

  • Authors:
  • Alexander Shen;Nikolai Vereshchagin

  • Affiliations:
  • Independent Univ. of Moscow, Moscow, Russia;Moscow State Univ., Moscow, Russia

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

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Abstract

Conditional Kolmogorov complexity K(x|y) can be understood as the complexity of the problem "Y→X", where X is the problem "construct x" and Y is the problem "construct y". Other logical operations (↑, ↓, ↔) can be interpreted in a similar way, extending Kolmogorov interpretation of intuitionistic logic and Kleene realizability. This leads to interesting problems in algorithmic information theory. Some of these questions are discussed.