Abstract
In this paper, we propose an architecture of oritatami systems with which one can simulate an arbitrary nondeterministic finite automaton (NFA) in a unified manner. The oritatami system is known to be Turing-universal but the simulation available so far requires 542 bead types and \(O(t^4 \log ^2 t)\) steps in order to simulate t steps of a Turing machine. The architecture we propose employs only 329 bead types and requires just \(O(t |Q|^4 |\varSigma |^2)\) steps to simulate an NFA with a state set Q working on a word of length t over an alphabet \(\varSigma \).
This work is supported primarily by JSPS-NRF Bilateral Program No. YB29004 to Han and Seki, the Basic Science Research Program (NRF-2018R1D1A1A09084107) to Han, JSPS KAKENHI Grant-in-Aids for Young Scientists (A) No. 16H05854 and for Challenging Research (Exploratory) No. 18K19779 to Seki, and JST Program to Disseminate Tenure Tracking System, MEXT, Japan No. 6F36 to Seki.
Kim is also supported by NIH R01GM109459, NSF’s CCF01526485, DMS-1800443, the Southeast Center for Mathematics and Biology, and the NSF-Simons Research Center for Mathematics of Complex Biological Systems (DMS-1764406, 594594).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A periodic transcript is likely to be able to be transcribed from a circular DNA [3].
References
Allouche, J.P., Shallit, J.: Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003)
Demaine, E.D., et al.: Know when to fold ’Em: self-assembly of shapes by folding in Oritatami. In: Doty, D., Dietz, H. (eds.) DNA 2018. LNCS, vol. 11145, pp. 19–36. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00030-1_2
Geary, C.W., Andersen, E.S.: Design principles for single-stranded RNA Origami structures. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 1–19. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11295-4_1
Geary, C.W., Meunier, P., Schabanel, N., Seki, S.: Programming biomolecules that fold greedily during transcription. In: MFCS 2016. LIPIcs, vol. 58, pp. 43:1–43:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016)
Geary, C.W., Meunier, P., Schabanel, N., Seki, S.: Proving the Turing universality of Oritatami co-transcriptional folding. In: Hsu, W., Lee, D., Liao, C. (eds.) ISAAC 2018. LIPIcs, vol. 123, pp. 23:1–23:13. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.ISAAC.2018.23
Geary, C.W., Rothemund, P.W.K., Andersen, E.S.: A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345(6198), 799–804 (2014). https://doi.org/10.1126/science.1253920
Han, Y.-S., Kim, H.: Construction of geometric structure by Oritatami system. In: Doty, D., Dietz, H. (eds.) DNA 2018. LNCS, vol. 11145, pp. 173–188. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00030-1_11
Han, Y., Kim, H., Masuda, Y., Seki, S.: A general architecture of Oritatami systems for simulating arbitrary finite automata (2019). http://arxiv.org/abs/1904.10174
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_22
Watters, K., Strobel, E.J., Yu, A.M., Lis, J.T., Lucks, J.B.: Cotranscriptional folding of a riboswitch at nucleotide resolution. Nat. Struct. Mol. Biol. 23(12), 1124–1133 (2016). https://doi.org/10.1038/nsmb.3316
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Han, YS., Kim, H., Masuda, Y., Seki, S. (2019). A General Architecture of Oritatami Systems for Simulating Arbitrary Finite Automata. In: Hospodár, M., Jirásková, G. (eds) Implementation and Application of Automata. CIAA 2019. Lecture Notes in Computer Science(), vol 11601. Springer, Cham. https://doi.org/10.1007/978-3-030-23679-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-23679-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23678-6
Online ISBN: 978-3-030-23679-3
eBook Packages: Computer ScienceComputer Science (R0)