Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 407816, 7 pages
http://dx.doi.org/10.1155/2013/407816
Research Article

Solving Vertex Cover Problem Using DNA Tile Assembly Model

Key Laboratory of Image Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Received 13 October 2013; Accepted 15 November 2013

Academic Editor: Sabri Arik

Copyright © 2013 Zhihua Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, no. 5187, pp. 1021–1024, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. E. Winfree, Algorithmic self-assembly of DNA [Ph.D. thesis], California Institute of Technology, Pasadena, Calif, USA, 1998.
  3. J. H. Reif, S. Sahu, and P. Yin, “Compact error-resilient computational DNA tiling assemblies,” in Proceedings of the 10th International Workshop on DNA Computing, pp. 293–307, June 2004. View at Scopus
  4. P. W. K. Rothemund, N. Papadakis, and E. Winfree, “Algorithmic self-assembly of DNA sierpinski triangles,” PLoS Biology, vol. 2, no. 12, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Pǎun, Membrane Computing: an Introduction, Springer, Berlin, Germany, 2002.
  6. G. Pǎun, G. Rozenberg, and A. Salomaa, Eds., The Oxford Handbook of Membrane Computing, Oxford University Press, 2010.
  7. G. Pǎun, “Computing with membranes,” Journal of Computer and System Sciences, vol. 61, no. 1, pp. 108–143, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. T. Song, L. Pan, K. Jiang, B. Song, and W. Chen, “Normal forms for some classes of sequential spiking neural P systems,” IEEE Transactions on Nanobioscience, vol. 12, no. 3, pp. 255–264, 2013. View at Google Scholar
  9. J. Wang, H. J. Hoogeboom, L. Pan, G. Pǎun, and M. J. Pérez-Jiménez, “Spiking neural P systems with weights,” Neural Computation, vol. 22, no. 10, pp. 2615–2646, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. T. Song, L. Pan, J. Wang, I. Venkat, K. G. Subramanian, and R. Abdullah, “Normal forms of spiking neural P systems with anti-spikes,” IEEE Transactions on NanoBioscience, vol. 11, no. 4, pp. 352–359, 2012. View at Google Scholar
  11. L. Pan and G. Pǎun, “Spiking neural P systems: an improved normal form,” Theoretical Computer Science, vol. 411, no. 6, pp. 906–918, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. T. Song, L. Pan, and G. Pǎun, “Asynchronous spiking neural P systems with local synchronization,” Information Sciences, vol. 219, pp. 197–207, 2012. View at Google Scholar
  13. L. Adleman, P. K. M. Rothemund, S. Roweis, and E. Winfree, “On applying molecular computation to the data encryption standard,” in Proceedings of the 2nd Annual Meeting on DNA Computers, pp. 10–12, Princeton, NJ, USA, 1996.
  14. R. S. Braich, N. Chelyapov, C. Johnson, P. W. K. Rothemund, and L. Adleman, “Solution of a 20-variable 3-SAT problem on a DNA computer,” Science, vol. 296, no. 5567, pp. 499–502, 2002. View at Publisher · View at Google Scholar · View at Scopus
  15. J.-M. Lehn, “Supramolecular chemistry,” Science, vol. 260, no. 5115, pp. 1762–1763, 1993. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Mao, T. H. LaBean, J. H. Reif, and N. C. Seeman, “Logical computation using algorithmic self-assembly of DNA triple-crossover molecules,” Nature, vol. 407, no. 6803, pp. 493–496, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. R. D. Barish, P. W. K. Rothemund, and E. Winfree, “Two computational primitives for algorithmic self-assembly: copying and counting,” Nano Letters, vol. 5, no. 12, pp. 2586–2592, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Rothemund and E. Winfree, “The program-size complexity of self-assembled squares,” in Proceedings of ACM Symposium on Theory of Computing (STOC '02), pp. 459–468, Quebec, Canad, May 2000.
  19. Y. Brun, “Arithmetic computation in the tile assembly model: addition and multiplication,” Theoretical Computer Science, vol. 378, no. 1, pp. 17–31, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus