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Multiplier System in the Tile Assembly Model with Reduced Tileset-Size

  • Xiwen Fang
  • Xuejia Lai
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 237)

Abstract

Previously a 28-tile multiplier system which computes the product of two numbers was proposed by Brun. However the tileset-size is not optimal. In this paper we prove that multiplication can be carried out using less tile types while maintaining the same time efficiency: we propose two new tile assembly systems, both can deterministically compute A*B for given A and B in constant time. Our first system requires 24 computational tile types while our second system requires 16 tile types, which achieve smaller constants than Brun’s 28-tile multiplier system.

Keywords

tile assembly model DNA computing multiplier tileset-size 

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References

  1. 1.
    Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Lipton, R.: Using dna to solve np-complete problems. Science 268(4) (1995)Google Scholar
  3. 3.
    Liu, Q., Wang, L., Frutos, A., Condon, A., Corn, R., Smith, L., et al.: Dna computing on surfaces. Nature 403(6766), 175–179 (2000)CrossRefGoogle Scholar
  4. 4.
    Ouyang, Q., Kaplan, P., Liu, S., Libchaber, A.: Dna solution of the maximal clique problem. Science 278(5337), 446–449 (1997)CrossRefGoogle Scholar
  5. 5.
    Rothemund, P., Winfree, E.: The program-size complexity of self-assembled squares. In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 459–468. ACM (2000)Google Scholar
  6. 6.
    Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (1998)Google Scholar
  7. 7.
    Winfree, E., Liu, F., Wenzler, L., Seeman, N., et al.: Design and self-assembly of two-dimensional dna crystals. Nature 394(6693), 539–544 (1998)CrossRefGoogle Scholar
  8. 8.
    Barish, R., Rothemund, P., Winfree, E.: Two computational primitives for algorithmic self-assembly: Copying and counting. Nano Letters 5(12), 2586–2592 (2005)CrossRefGoogle Scholar
  9. 9.
    Rothemund, P., Papadakis, N., Winfree, E.: Algorithmic self-assembly of dna sierpinski triangles. PLoS Biology 2(12), e424 (2004)Google Scholar
  10. 10.
    Brun, Y.: Solving np-complete problems in the tile assembly model. Theoretical Computer Science 395(1), 31–46 (2008)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Brun, Y.: Improving efficiency of 3-SAT-solving tile systems. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 1–12. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Lagoudakis, M., LaBean, T.: 2-d dna self-assembly for satisfiability. In: DNA Based Computers V, vol. 54, pp. 141–154 (2000)Google Scholar
  13. 13.
    Brun, Y.: Arithmetic computation in the tile assembly model: Addition and multiplication. Theoretical Computer Science 378(1), 17–31 (2007)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xiwen Fang
    • 1
  • Xuejia Lai
    • 1
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina

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