On the Length of Programs for Computing Finite Binary Sequences: statistical considerations

  • Authors:
  • Gregory J. Chaitin

  • Affiliations:
  • Mario Bravo 249, Buenos Aires and Buenos Aires, Argentina

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1969

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Abstract

An attempt is made to carry out a program (outlined in a previous paper) for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining a random or patternless, infinite binary sequence to be a sequence whose initial segments are all random or patternless finite binary sequences. A definition based on the bounded-transfer Turing machine is given detailed study, but insufficient understanding of this computing machine precludes a complete treatment. A computing machine is introduced which avoids these difficulties.