Version 1
: Received: 19 September 2024 / Approved: 20 September 2024 / Online: 20 September 2024 (05:20:03 CEST)
Version 2
: Received: 30 September 2024 / Approved: 1 October 2024 / Online: 3 October 2024 (08:55:32 CEST)
Version 3
: Received: 11 October 2024 / Approved: 12 October 2024 / Online: 14 October 2024 (03:33:03 CEST)
How to cite:
Bieniawski, W.; Masierak, P.; Tomski, A.; Łukaszyk, S. On the Salient Regularities of Strings of Assembly Theory. Preprints2024, 2024091581. https://doi.org/10.20944/preprints202409.1581.v3
Bieniawski, W.; Masierak, P.; Tomski, A.; Łukaszyk, S. On the Salient Regularities of Strings of Assembly Theory. Preprints 2024, 2024091581. https://doi.org/10.20944/preprints202409.1581.v3
Bieniawski, W.; Masierak, P.; Tomski, A.; Łukaszyk, S. On the Salient Regularities of Strings of Assembly Theory. Preprints2024, 2024091581. https://doi.org/10.20944/preprints202409.1581.v3
APA Style
Bieniawski, W., Masierak, P., Tomski, A., & Łukaszyk, S. (2024). On the Salient Regularities of Strings of Assembly Theory. Preprints. https://doi.org/10.20944/preprints202409.1581.v3
Chicago/Turabian Style
Bieniawski, W., Andrzej Tomski and Szymon Łukaszyk. 2024 "On the Salient Regularities of Strings of Assembly Theory" Preprints. https://doi.org/10.20944/preprints202409.1581.v3
Abstract
Using assembly theory of strings of any natural radix b we find some of their salient regularities. In particular, we show that the upper bound of the assembly index depends on the radix b both quantitatively and qualitatively, and the longest length N of a string that has the assembly index of N-k is given by N(N-k)=b2+b+3k-2 for k={1,2,3,4}. We also provide particular forms of such strings. For k=1 such odd length strings are nearly balanced and there are four such different strings if b=2 and seventy-two if b=3. The assembly depth of a string has a value between the minimum assembly index for the length of this string and the assembly index of this string. Since these results are valid also for b=1, assembly theory subsumes information theory.
Keywords
assembly theory; information theory; complexity measures; information entropy; mathematical physics
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.