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Complexity of majorants

Logic 2020-12-29 v2 Information Theory math.IT

Abstract

The minimal Kolmogorov complexity of a total computable function that exceeds everywhere all total computable functions of complexity at most nn, is 2n+O(1)2^{n+O(1)}. If we replace "everywhere" by "for all sufficiently large inputs", the answer is n+O(1)n+O(1).

Cite

@article{arxiv.2004.02844,
  title  = {Complexity of majorants},
  author = {Alexander Shen},
  journal= {arXiv preprint arXiv:2004.02844},
  year   = {2020}
}
R2 v1 2026-06-23T14:41:31.000Z