Advertisement

Counting Infinitely by Oritatami Co-transcriptional Folding

  • Kohei MaruyamaEmail author
  • Shinnosuke Seki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

A fixed bit-width counter was proposed as a proof-of-concept demonstration of an 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.

References

  1. 1.
    Adleman, L., Chang, Q., Goel, A., Huang, M.D.: Running time and program size for self-assembled squares. In: Proceedings of the STOC 2001, pp. 740–748. ACM (2001)Google Scholar
  2. 2.
    Bryans, N., Chiniforooshan, E., Doty, D., Kari, L., Seki, S.: The power of nondeterminism in self-assembly. Theory Comput. 9, 1–29 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Evans, C.G.: Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly. Ph.D. thesis, Caltech (2014)Google Scholar
  4. 4.
    Geary, C., Étienne Meunier, P., Schabanel, N., Seki, S.: Proving the turing universality of oritatami co-transcriptional folding. In: Proceedings of the ISAAC 2018, pp. 23:1–23:13 (2018)Google Scholar
  5. 5.
    Geary, C., Étienne Meunier, P., Schabanel, N., Seki, S.: Oritatami: a computational model for molecular co-transcriptional folding. Int. J. Mol. Sci. 20(9), 2259 (2019)CrossRefGoogle Scholar
  6. 6.
    Geary, C., Rothemund, P.W.K., Andersen, E.S.: A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345(6198), 799–804 (2014)CrossRefGoogle Scholar
  7. 7.
    Masuda, Y., Seki, S., Ubukata, Y.: Towards the algorithmic molecular self-assembly of fractals by cotranscriptional folding. In: Câmpeanu, C. (ed.) CIAA 2018. LNCS, vol. 10977, pp. 261–273. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-94812-6_22CrossRefzbMATHGoogle Scholar
  8. 8.
    McClung, C.R.: Plant circadian rhythms. Plant Cell 18, 792–803 (2006)CrossRefGoogle Scholar
  9. 9.
    Minsky, M. (ed.): Computation: Finite and Infinite Machines. Prentice-Hall Inc., Upper Saddle River (1967)zbMATHGoogle Scholar
  10. 10.
    Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the STOC 2000, pp. 459–468. ACM (2000)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.The University of Electro-CommunicationsChofuJapan
  2. 2.École Normale Superiéure de LyonLyonFrance

Personalised recommendations