Automatic Kolmogorov complexity, normality, and finite-state dimension revisited

Kozachinskiy, Alexander; Shen, Alexander

doi:10.1016/j.jcss.2020.12.003

Cited by 5 publications

(2 citation statements)

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“…It then traverses a loop for 1v 62 (d 62 ) 30 0 61 . It then reads 0 3 and enters a loop for the string (1v 63 0 63 ) 21 . Following this it reads 01v 64 0 63 and then enters a loop for the string (1v 64 0 63 ) 7 .…”

Section: Discussion On Lower Bounds For Champernowne Sequencesmentioning

confidence: 99%

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Normal Sequences with Non-Maximal Automatic Complexity

Jordon,

Moser

2021

Preprint

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This paper examines Automatic Complexity, a complexity notion introduced by Shallit and Wang in 2001 [28]. We demonstrate that there exists a normal sequence T such that I(T ) = 0 and S(T ) ≤ 1/2, where I(T ) and S(T ) are the lower and upper automatic complexity rates of T respectively. We furthermore show that there exists a Champernowne sequence C, i.e. a sequence formed by concatenating all strings of length 1 followed by concatenating all strings of length 2 and so on, such that S(C) ≤ 2/3.

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Section: Discussion On Lower Bounds For Champernowne Sequencesmentioning

confidence: 99%

“…A binary sequence is normal number in the sense of Borel [3] if for all n, every string of length n occurs as a substring in the sequence with limiting frequency 2 −n . The complexity of normal sequences has been widely studied in the finite-state setting for many years and a review of several old and new results can be found in [21].…”

Section: Introductionmentioning

confidence: 99%