On the Salient Limits of Strings of Assembly Theory

Wawrzyniec Bieniawski; Piotr Masierak; Szymon Łukaszyk; Andrzej Tomski

doi:10.20944/preprints202409.1581.v2

Preprint Article Version 2 This version is not peer-reviewed

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)

We consider the formation of strings of any natural radix b within the framework of assembly theory. 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}. We also provide two 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. Since these results are valid also for b=1, assembly theory subsumes information theory.

assembly theory; information theory; complexity measures; information entropy; mathematical physics

Physical Sciences, Mathematical Physics

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On the Salient Limits of Strings of Assembly Theory

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