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Counting infinitely by oritatami co-transcriptional folding

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Abstract

A fixed bit-width counter was proposed as a proof-of-concept demonstration of the oritatami model of cotranscriptional folding [Geary et al., Proc. MFCS 2016, LIPIcs 58, 43:1-43:14], and it was embedded into another oritatami system that self-assembles a finite portion of Heighway dragon fractal. In order to expand its applications, we endow this counter with capability to widen bit-width at every encounter with overflow.

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Notes

  1. A video to show how a glider folds can be found at https://www.dailymotion.com/video/x3cdj35, in which the Turing universal oritatami system by Geary et al. (2018) is running at delay 3.

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Acknowledgements

This work is supported in part by KAKENHI Grant-in-Aid for Challenging Research (Exploratory) No. 18K19779, for Scientific Research (B) No. 20H04141, and Scientific Research (C) No. 20K11672, and JST Program to Disseminate Tenure Tracking System No. 6F36, both granted to S. S.

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Correspondence to Shinnosuke Seki.

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An extended abstract on this work was published as a short paper in the proceedings of the 46th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2020, Limassol, Cyprus, January 20-24, 2020), Lecture Notes in Computer Science (LNCS) 12011, pp. 566–575.

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Maruyama, K., Seki, S. Counting infinitely by oritatami co-transcriptional folding. Nat Comput 20, 329–340 (2021). https://doi.org/10.1007/s11047-021-09842-6

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