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A Highly Random Number

  • Verónica Becher
  • Sergio Daicz
  • Gregory Chaitin
Conference paper
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Abstract

In his celebrated 1936 paper Turing defined a machine to be circular iff it performs an infinite computation outputting only finitely many symbols. We define α as the probability that an arbitrary machine be circular and we prove that α is a random number that goes beyond Ω, the probability that a universal self delimiting machine halts. The algorithmic complexity of α is strictly greater than that of Ω, but similar to the algorithmic complexity of Ω', the halting probability of an oracle machine. What makes α interesting is that it is an example of a highly random number definable without considering oracles.

Keywords

Algorithmic Complexity Minimal Program Computable Number Program Size Universal Machine 
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-Verlag London Limited 2001

Authors and Affiliations

  • Verónica Becher
    • 1
  • Sergio Daicz
    • 1
  • Gregory Chaitin
    • 2
  1. 1.Departamento de Computación, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresArgentina
  2. 2.IBM Thomas J. Watson Research CenterUSA

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