On the Gap Between Trivial and Nontrivial Initial Segment Prefix-Free Complexity

  title={On the Gap Between Trivial and Nontrivial Initial Segment Prefix-Free Complexity},
  author={Martijn Baartse and George Barmpalias},
  journal={Theory of Computing Systems},
An infinite sequence X is said to have trivial (prefix-free) initial segment complexity if the prefix-free Kolmogorov complexity of each initial segment of X is the same as the complexity of the sequence of 0s of the same length, up to a constant. We study the gap between the minimum complexity K(0 n ) and the initial segment complexity of a nontrivial sequence, and in particular the nondecreasing unbounded functions f such that ⋆ for a nontrivial sequence X, where K denotes the prefix-free… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 24 references


  • Barbara F. Csima, Antonio Montalbán. A minimal pair of K-degrees. Proc. Amer
  • Soc., 134(5):1499–1502 (electronic),
  • 2006
Highly Influential
4 Excerpts

Formal Logic

  • George Barmpalias. Relative randomness, J cardinality.NotreDame
  • 51(2),
  • 2010
2 Excerpts


  • George Barmpalias. Compactness arguments with effectively randomness
  • Logic Computation,
  • 2010

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