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
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.
References
Adleman L, Chang Q, Goel A, Huang M.D (2001) Running time and program size for self-assembled squares. In: Proceedings of STOC 2001, ACM. pp 740–748
Bryans N, Chiniforooshan E, Doty D, Kari L, Seki S (2013) The power of nondeterminism in self-assembly. Theory Comput 9:1–29
Demaine ED, Hendricks J, Olsen M, Patitz MJ, Rogers TA, Schabanel N, Seki S, Thomas H (2018) Know when to fold ’em: Self-assembly of shapes by folding in oritatami. In: Proceedings of DNA24. LNCS, vol. 11145, pp 19–36. Springer
Elonen A (2016) Molecular folding and computation. Bachelor Thesis
Evans CG (2014) Crystals that Count! Physical Principles and Experimental Investigations of DNA Tile Self-Assembly. Ph.D. thesis, Caltech
Geary C, Andersen ES (2014) Design principles for single-stranded RNA origami structures. In: Proceedings of DNA 20. LNCS, vol. 8727, pp 1–19. Springer
Geary C, Étienne Meunier P, Schabanel N, Seki S (2018) Proving the Turing universality of oritatami cotranscriptional folding. In: Proceedings of ISAAC 2018. LIPIcs, vol. 123, pp. 23:1–23:13
Geary C, Étienne Meunier P, Schabanel N, Seki S (2019) Oritatami: A computational model for molecular co-transcriptional folding. Int. J. Mol. Sci. 20(9):2259 (preliminary version published in MFCS 2016)
Geary C, Rothemund PWK, Andersen ES (2014) A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345(6198):799–804
Han YS, Kim H (2018) Construction of geometric structure by oritatami system. In: Proceedings of DNA24. LNCS, vol. 11145, pp 173–188. Springer
Han YS, Kim H (2019) Ruleset optimization on isomorphic oritatami systems. Theor Comput Sci 785:128–139
Lathrop JI, Lutz JH, Patitz MJ, Summers SM (2011) Computability and complexity in self-assembly. Theory Comput Syst 48(3):617–647
Masuda Y, Seki S, Ubukata Y (2018) Towards the algorithmic molecular self-assembly of fractals by cotranscriptional folding. In: Proceedings of CIAA 2018. LNCS, vol. 10977, pp 261–273. Springer
McClung CR (2006) Plant circadian rhythms. The Plant Cell 18:792–803
Minsky M (ed.) (1967) Computation: Finite and Infinite Machines. Prentice-Hall, Inc
Ota M, Seki S (2017) Ruleset design problems for oritatami systems. Theor Comput Sci 671:26–35
Pchelina D, Schabanel N, Seki S, Ubukata Y (2020) Simple intrinsic simulation of cellular automata in oritatami molecular folding model. In: Proc. LATIN 2020. LNCS, vol. 12118, pp 425–436. Springer
Rothemund PWK, Winfree E (2000) The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of STOC 2000, ACM. pp 459–468
Winfree E (1998) Algorithmic Self-Assembly of DNA. Ph.D. thesis, Caltech
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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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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DOI: https://doi.org/10.1007/s11047-021-09842-6