Skip to main content
SpringerLink
Log in

Reversible Computation Using Swap Reactions on a Surface

  • Conference paper
  • First Online:
DNA Computing and Molecular Programming (DNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11648))

Included in the following conference series:

  • 1188 Accesses

Abstract

Chemical reaction networks (CRNs) and DNA strand displacement systems have shown potential for implementing logically and physically reversible computation. It has been shown that CRNs on a surface allow highly scalable and parallelizable computation. In this paper, we demonstrate that simple rearrangement reactions on a surface, which we refer to as swaps, are capable of physically reversible Boolean computation. We present designs for elementary logic gates, a method for constructing arbitrary feedforward digital circuits, and a proof of their correctness.

T. Brailovskaya, G. Gowri and S. Yu—Equal contribution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)

    Article  MathSciNet  Google Scholar 

  2. Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)

    Article  MathSciNet  Google Scholar 

  3. Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21, 219–253 (1982)

    Article  MathSciNet  Google Scholar 

  4. Margolus, N.: Physics-like models of computation. Phys. D Nonlinear Phenom. 10, 81–95 (1984)

    Article  MathSciNet  Google Scholar 

  5. D’Souza, R.M., Homsy, G.E., Margolus, N.H.: Simulating digital logic with the reversible aggregation model of crystal growth. In: Griffeath, D., Moore, C. (eds.) New Constructions in Cellular Automata, pp. 211–230. Oxford University Press, Oxford (2003)

    Google Scholar 

  6. Ouldridge, T.E.: The importance of thermodynamics for molecular systems, and the importance of molecular systems for thermodynamics. Nat. Comput. 17, 3–29 (2018)

    Article  MathSciNet  Google Scholar 

  7. Wolpert, D.: The stochastic thermodynamics of computation. J. Phys. Math. Theor. 52, 193001 (2019)

    Article  MathSciNet  Google Scholar 

  8. Perumalla, K.S.: Introduction to Reversible Computing. Chapman and Hall/CRC, Boca Raton (2013)

    Book  Google Scholar 

  9. Bennett, C.H.: The thermodynamics of computation-a review. Int. J. Theor. Phys. 21, 905–940 (1982)

    Article  Google Scholar 

  10. Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107, 5393–5398 (2010)

    Article  Google Scholar 

  11. Chen, Y.-J., et al.: Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013)

    Article  Google Scholar 

  12. Srinivas, N., Parkin, J., Seelig, G., Winfree, E., Soloveichik, D.: Enzyme-free nucleic acid dynamical systems. Science 358, eaal2052 (2017)

    Article  Google Scholar 

  13. Thachuk, C., Condon, A.: Space and energy efficient computation with DNA strand displacement systems. In: Stefanovic, D., Turberfield, A. (eds.) DNA 2012. LNCS, vol. 7433, pp. 135–149. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32208-2_11

    Chapter  MATH  Google Scholar 

  14. Codon, A., Hu, A.J., Manuch, J., Thachuk, C.: Less haste, less waste: on recycling and its limits in strand displacement systems. Interface Focus 2, 512–521 (2012)

    Article  Google Scholar 

  15. Condon, A., Thachuk, C.: Towards space- and energy-efficient computations. In: Kempes, C., Grochow, J., Stadler, P., Wolpert, D. (eds.) The Energetics of Computing in Life and Machines, Chap. 9, pp. 209–232. The Sante Fe Institute Press, Sante Fe (2019)

    Google Scholar 

  16. Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with DNA polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18305-8_12

    Chapter  MATH  Google Scholar 

  17. Qian, L., Winfree, E.: Parallel and scalable computation and spatial dynamics with DNA-based chemical reaction networks on a surface. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 114–131. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11295-4_8

    Chapter  MATH  Google Scholar 

  18. Goldschlager, L.M.: The monotone and planar circuit value problems are log space complete for P. ACM SIGACT News 9, 25–29 (1977)

    Article  Google Scholar 

  19. Masson, G.M., Gingher, G.C., Nakamura, S.: A sampler of circuit switching networks. Computer 12, 32–48 (1979)

    Article  Google Scholar 

  20. Savage, J.E.: Models of Computation. Addison-Wesley, Reading (1998). Section 12.6

    MATH  Google Scholar 

  21. Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011)

    Article  Google Scholar 

  22. Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)

    MATH  Google Scholar 

  23. Johnson, R.F., Dong, Q., Winfree, E.: Verifying chemical reaction network implementations: a bisimulation approach. Theor. Comput. Sci. 765, 3–46 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Support from National Science Foundation grant CCF-1317694 is gratefully acknowledged. We also thank Lulu Qian and Chris Thachuk for helpful discussion and comments.

Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, USA

    Tatiana Brailovskaya, Gokul Gowri, Sean Yu & Erik Winfree

Authors
  1. Tatiana Brailovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gokul Gowri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sean Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Erik Winfree
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gokul Gowri .

Editor information

Editors and Affiliations

  1. California Institute of Technology, Pasadena, CA, USA

    Chris Thachuk

  2. Arizona State University, Tempe, AZ, USA

    Yan Liu

Appendix

Appendix

Fig. 11.
figure 11

Paint functions for the NOT gate. All species in the stochastic CRN that corresponds to the NOT gate as well as their associated paint functions are shown. In each table, the left hand column is the list of species. Each row is a paint function for a particular species. Each column represents how a particular lattice is painted. (a) Initial configuration of the NOT gate with each lattice point labeled with a row number and a column letter. (b) Paint function for B. (c) Paint function for \(A^{(0)}\) including \(A_S\). (d) Paint function for \(A^{(1)}\) excluding \(A_S\). (e) Stochastic CRN equivalent to the NOT gate.

Full size image
Fig. 12.
figure 12

Paint functions and the stochastic CRN for the AND gate. (a) Initial AND gate surface layout with each lattice labeled with a row number and a column letter. (b) Paint function for \(A^{(1)}\). (c) Paint function for D. (d) Paint function for B. (e) Paint function for C. (f) Paint function for \(A^{(0)}\). (g) Stochastic CRN equivalent to AND gate.

Full size image
Fig. 13.
figure 13

Paint functions for the fanout gate. (a) Initial configuration of the fanout gate with each lattice labeled with a row number and a column letter. (b) Paint function for A. (c) Paint function for B. (d) Paint function for \(C^{(1)}\) including \(C_S\). (e) Paint function for \(C^{(0)}\) excluding \(C_S\). (f) Stochastic CRN equivalent to fanout.

Full size image
Fig. 14.
figure 14

Paint function for partial wirecross. Truncated portions are equivalent to trajectories found in AND/OR/NOT gates. (a) Initial configuration of the central portion of wirecross with each lattice labeled with a row number and a column letter. (b) Paint function for A. (c) Paint function for B. (d) Paint function for C. (e) Paint function for D. (f) Stochastic CRN equivalent to central portion of wirecross.

Full size image

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Brailovskaya, T., Gowri, G., Yu, S., Winfree, E. (2019). Reversible Computation Using Swap Reactions on a Surface. In: Thachuk, C., Liu, Y. (eds) DNA Computing and Molecular Programming. DNA 2019. Lecture Notes in Computer Science(), vol 11648. Springer, Cham. https://doi.org/10.1007/978-3-030-26807-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26807-7_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26806-0

  • Online ISBN: 978-3-030-26807-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation