Skip to main content
SpringerLink
Log in

DNA computing: Arrival of biological mathematics

The most highly parallelized computers

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. L. Adleman, Molecular computation of solutions to combinatorial problems,Science 266 (Nov. 1994), pp. 1021–1024.

    Article  Google Scholar 

  2. L. Adleman, On constructing a molecular computer,ftp://us.edu/ pub/csinfo/papers/adleman.

  3. L. Adleman, P. Rothemund, S. Roweis, and E. Winfree, On applying molecular computation to the Data Encryption Standard, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 28–48.

  4. J. Amenyo, Mesoscopic computer engineering: Automating DNA-based molecular computing via traditional practices of parallel computer architecture design, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 217–235.

  5. M. Amos, A. Gibbons, and D. Hodgson, Error-resistant implementation of DNA computation, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 87–101.

  6. E. Baum, Building an associative memory vastly larger than the brain.Science 268 (April 1995), 583–585.

    Article  Google Scholar 

  7. E. Baum, DNA sequences useful for computation,Proceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 122–127.

  8. D. Beaver, Computing with DNA,J. Computat. Biol. 2(1) (1995).

  9. D. Beaver, A universal molecular computer,http://www.transarc. com/~beaver/research/alternative/molecute/molec.html.

  10. D. Boneh, R. Lipton, and C. Dunworth, Breaking DES using a molecular computer,http://www.cs.princeton.edu/~dabo.

  11. D. Boneh, R. Lipton, C. Dunworth, and J. Sgall, On the computational power of DNA,http://www.cs.princeton.edu/~dabo.

  12. D. Boneh, C. Dunworth, J. Sgall, and R. Lipton, Making DNA computers error resistant, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 102–110.

  13. R. Deaton, R. Murphy, M. Garzon, D. Franceschetti, and S. Stevens, Good encodings for DNA-based solutions to combinatorial problems, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 131–140.

  14. K.L. Deninnghoff and R.W. Gatterdam, On the undecidability of splicing systems,Int. J. Computer Math. 27 (1989), pp. 133–145.

    Article  Google Scholar 

  15. C. Ferretti, S. Kobayashi, and T. Yokomori, DNA splicing systems and Post Systems, inFirst Annual Pacific Symposium on Biocomputing, 1996.

  16. R. Freund, L. Kari, and G. Paun, DNA computing based on splicing: the existence of universal computers,http://www.csd.uwo. cal~lila.

  17. M. Garey and D. Johnson,Computers and Intractability. A Guide to the Theory of NP-completeness, San Francisco: W.H. Freeman and Company (1979).

    MATH  Google Scholar 

  18. R.W. Gatterdam, DNA and twist free splicing systems, inWords, Languages and Combinatorics II, (M. Ito and H. Jürgensen, eds.), Singapore, World Scientific Publishers (1994), pp. 170–178.

    Google Scholar 

  19. D.K. Gifford, On the path to computation with DNA.Science 266 (Nov. 1994), pp. 993–994.

    Article  Google Scholar 

  20. F. Guarnieri and C. Bancroft, Use of a horizontal chain reaction for DNA-based addition, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 249–259.

  21. J. Hartmanis, On the weight of computations.Bull. Eur. Assoc. Theoret. Computer Sci. 55 (1995), pp. 136–138.

    MATH  Google Scholar 

  22. T. Head, Formal language theory and DNA: An analysis of the generative capacity of recombinant behaviors.Bull. Math. Biol. 49 (1987), pp. 737–759.

    Article  MATH  MathSciNet  Google Scholar 

  23. D. Hofstadter,Gödel, Escher, Bach: An Eternal Golden Braid, New York: Basic Books (1979).

    Google Scholar 

  24. F. Hoppensteadt, Getting started in mathematical biology,Notices AMS 42 (9) (1995).

  25. N. Jonoska and S. Karl, A molecular computation of the road coloring problem, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 148–158.

  26. P. Kaplan, G. Cecchi, and A. Libchaber, DNA-based molecular computation: Template-template interactions in PCR, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 159-171.

  27. L. Kari, DNA computers: Tomorrow’s reality.Bull. Eur. Assoc. Theoret. Computer Sci. 59 (1996), pp. 256–266.

    Google Scholar 

  28. L. Kari and G. Thierrin, Contextual insertions/deletions and computability,Inform. Computat. 131, no. 1 (1996), pp. 47–61.

    Article  MATH  MathSciNet  Google Scholar 

  29. J. Kendrew, et al. (eds.),The Encyclopedia of Molecular Biology, Oxford: Blackwell Science (1994).

    Google Scholar 

  30. S. Kurtz, S. Mahaney, J. Royer, and J. Simon, Active transport in biological computing, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 111–121.

  31. T. Leete, M. Schwartz, R. Williams, D. Wood, J. Salem, and H. Rubin, Massively parallel DNA computation: Expansion of symbolic determinants, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 49–66.

  32. R. Lipton, DNA solution of hard computational problems,Science 268 (April 1995), pp. 542–545.

    Article  Google Scholar 

  33. Q. Liu, Z. Guo, A. Condon, R. Corn, M. Lagally, and L. Smith, A surface-based approach to DNA computation, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 206–216.

  34. K. Mir, A restricted genetic alphabet for DNA computing, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 128–130.

  35. D. Morris,Intimate Behavior, New York: Random House (1971).

    Google Scholar 

  36. J. Oliver, Computation with DNA: Matrix multiplication, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 236–248.

  37. G. Paun, On the splicing operation,Discrete Appl. Math. 70 (1996), pp. 57–79.

    Article  MATH  MathSciNet  Google Scholar 

  38. G. Paun, On the power of the splicing operation,Int. J. Computer Math. 59 (1995), pp. 27–35.

    Article  MATH  Google Scholar 

  39. G. Paun and A. Salomaa, DNA computing based on the splicing operation,Math. Japon. 43 (3) (1996), pp. 607–632.

    MATH  MathSciNet  Google Scholar 

  40. Proceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996).

  41. Plato,Great Dialogues of Plato, New York: The New American Library (1956).

    Google Scholar 

  42. J. Reif, Parallel molecular computation: models and simulation. in SPAA’95 (to appear); also athttp://www.cs.duke.edu/~reif/ HomePage. html.

  43. P. Rothemund, A DNA and restriction enzyme implementation of Turing machines, abstract athttp://www.ugcs.caltech.edu/~pwkr/ oett.html.

  44. S. Roweis, E. Winfree, R. Burgoyne, N. Chelyapov, M. Goodman, P. Rothemund, and L. Adleman, A sticker based architecture for DNA computation, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 1–27.

  45. A. Salomaa,Formal Languages, New York: Academic Press (1973).

    MATH  Google Scholar 

  46. L Seneca,Letters from a Stoic, Harmondsworth: Penguin (1969).

    Google Scholar 

  47. W. Smith and A. Schweitzer, DNA computers in vitro and in vivo, NEC Technical Report 3/20/95 (1995).

  48. A.M. Turing, On computable numbers, with an application to the Entscheidungsproblem,Proc. London Math. Soc. Ser. 2, 42 (1936), pp. 230–265.

    MathSciNet  Google Scholar 

  49. A. Yasuhara,Recursive Function Theory and Logic, New York: Academic Press (1971).

    MATH  Google Scholar 

  50. R. Williams and D. Wood, Exascale computer algebra problems interconnect with molecular reactions and complexity theory, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 260–268.

  51. E. Winfree, On the computational power of DNA annealing and ligation,http://dope.caltech.edu/winfree/DNA.html.

  52. E. Winfree, X. Yang, and N. Seeman, Universal computation via self-assembly of DNA: Some theory and experiments, inProceedings of the 2nd DIMACS Workshop on DNA-Based Computers (1996), pp. 172–190.

  53. W. Wordsworth, The tables turned, inWordsworth’s Poems, (P. Wayne, ed.) London: Dent (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Lila Karl

Authors
  1. Lila Karl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lila Karl.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karl, L. DNA computing: Arrival of biological mathematics. The Mathematical Intelligencer 19, 9–22 (1997). https://doi.org/10.1007/BF03024425

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024425

Keywords

Search

Navigation