The frequent paucity of trivial strings

  title={The frequent paucity of trivial strings},
  author={Jack H. Lutz},
  • J. H. Lutz
  • Published 23 October 2013
  • Mathematics, Computer Science
  • ArXiv
A 1976 theorem of Chaitin can be used to show that arbitrarily dense sets of lengths n have a paucity of trivial strings (only a bounded number of strings of length n having trivially low plain Kolmogorov complexities). We use the probabilistic method to give a new proof of this fact. This proof is much simpler than previously published proofs, and it gives a tighter paucity bound. 
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