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

@article{Baartse2012OnTG,
  title={On the Gap Between Trivial and Nontrivial Initial Segment Prefix-Free Complexity},
  author={Martijn Baartse and George Barmpalias},
  journal={Theory of Computing Systems},
  year={2012},
  volume={52},
  pages={28-47}
}
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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