A Highly Random Number

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


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.


Algorithmic Complexity Minimal Program Computable Number Program Size Universal Machine 
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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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