eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
47:1
47:16
10.4230/LIPIcs.FSTTCS.2021.47
article
Normal Sequences with Non-Maximal Automatic Complexity
Jordon, Liam
1
https://orcid.org/0000-0003-0583-666X
Moser, Philippe
1
Department of Computer Science, Maynooth University, Maynooth, Ireland
This paper examines Automatic Complexity, a complexity notion introduced by Shallit and Wang in 2001 [Jeffrey O. Shallit and Ming-wei Wang, 2001]. 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 one followed by concatenating all strings of length two and so on, such that S(C) ≤ 2/3.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.47/LIPIcs.FSTTCS.2021.47.pdf
Automatic Complexity
finite-state complexity
normal sequences
Champernowne sequences
de Bruijn strings
Kolmogorov complexity