Dimension 1 sequences are close to randoms

Noam Greenberg, Joseph S. Miller, Alexander Shen, Linda Brown Westrick

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We show that a sequence has effective Hausdorff dimension 1 if and only if it is coarsely similar to a Martin-Löf random sequence. More generally, a sequence has effective dimension s if and only if it is coarsely similar to a weakly s-random sequence. Further, for any s<t, every sequence of effective dimension s can be changed on density at most H−1(t)−H−1(s) of its bits to produce a sequence of effective dimension t, and this bound is optimal.

Original languageEnglish (US)
Pages (from-to)99-112
Number of pages14
JournalTheoretical Computer Science
Volume705
DOIs
StatePublished - Jan 1 2018

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Effective Dimension
Random Sequence
If and only if
Hausdorff Dimension

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Greenberg, Noam ; Miller, Joseph S. ; Shen, Alexander ; Westrick, Linda Brown. / Dimension 1 sequences are close to randoms. In: Theoretical Computer Science. 2018 ; Vol. 705. pp. 99-112.
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Dimension 1 sequences are close to randoms. / Greenberg, Noam; Miller, Joseph S.; Shen, Alexander; Westrick, Linda Brown.

In: Theoretical Computer Science, Vol. 705, 01.01.2018, p. 99-112.

Research output: Contribution to journalArticle

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