Complexity of graph self-assembly in accretive systems and self-destructible systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3892 LNCS, Issue , 2006, Pages 257-274

  Reif, John H ^a   Sahu, Sudheer ^a   Yin, Peng ^a  

^a Duke University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTONOMOUS AGENTS; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; GRAPH THEORY; MATHEMATICAL MODELS; NANOTECHNOLOGY; PROBABILITY; RANDOM PROCESSES;

ACCRETIVE GRAPH ASSEMBLY PROBLEM (AGAP); ACCRETIVE SYSTEMS; BIOLOGICAL CONSTRUCTIONS; SELF-DESTRUCTIBLE SYSTEMS;

SELF ASSEMBLY;

EID: 33745763269     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11753681_21     Document Type: Conference Paper

References (44)

1. http://mrsec.wisc.edu/edetc/selfassembly/.
2. L. Adleman. Towards a mathematical theory of self-assembly. Technical Report 00-722, University of Southern California, 2000.
3. L. Adleman, Q. Cheng, A. Goel, and M.D. Huang. Running time and program size for self-assembled squares. In Proceedings of the thirty-third annual ACM symposium on Theory of computing, pages 740-748. ACM Press, 2001.
4. L. Adleman, Q. Cheng, A. Goel, M.D. Huang, D. Kempe, P.M. de Espans, and P.W.K. Rothemund. Combinatorial optimization problems in self-assembly. In Proceedings of the thirty-fourth annual ACM symposium on Theory of computing, pages 23-32. ACM Press, 2002.
5. L. Adleman, Q. Cheng, A. Goel, M.D. Huang, and H. Wasserman. Linear self-assemblies: Equilibria, entropy, and convergence rate. In Sixth International Conference on Difference Equations and Applications, 2001.
6. G. Aggarwal, M.H. Goldwasser, M. Y. Kao, and R.T. Schweller. Complexities for generalized models of self-assembly. In Proceedings of 15th annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 880-889. ACM Press, 2004.
7. N. Bowden, A. Terfort, J. Carbeck, and G.M. Whitesides. Self-assembly of mesoscale objects into ordered two-dimensional arrays. Science, 276(11):233-235, 1997.
8. R.F. Bruinsma, W.M. Gelbart, D. Reguera, J. Rudnick, and R. Zandi. Viral self-assembly as a thermodynamic process. Phys. Rev. Lett., 90(24):248101, 2003 June 20.
9. N. Chelyapov, Y. Brun, M. Gopalkrishnan, D. Reishus, B. Shaw, and L. Adleman. DNA triangles and self-assembled hexagonal tilings. J. Am. Chem. Soc., 126:13924-13925, 2004.
10. H.L. Chen, Q. Cheng, A. Goel, M.D. Huang, and P.M. de Espanes. Invariable self-assembly: Combining robustness with efficiency. In Proceedings of the 15th annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 890-899, 2004.
11. H.L. Chen and A. Goel. Error free self-assembly using error prone tiles. In DNA Based Computers 10, pages 274-283, 2004.
12. Q. Cheng, A. Goel, and P. Moisset. Optimal self-assembly of counters at temperature two. In Proceedings of the first conference on Foundations of nanoscience: self-assembled architectures and devices, 2004.
13. M. Cook, P.W.K. Rothemund, and E. Winfree. Self-assembled circuit patterns. In DNA Based Computers 9, volume 2943 of LNCS, pages 91-107, 2004.
14. K. Fujibayashi and S. Murata. A method for error suppression for self-assembling DNA tiles. In DNA Based Computing 10, pages 284-293, 2004.
15. Y. He, Y Chen, H. Liu, A.E. Ribbe, and C. Mao. Self-assembly of hexagonal DNA two-dimensional (2D) arrays. J. Am. Chem. Soc., 127:12202-12203, 2005.
16. N. Jonoska, S.A. Karl, and M. Saito. Three dimensional DNA structures in computing. BioSystems, 52:143-153, 1999.
17. N. Jonoska and G.L. McColm. A computational model for self-assembling flexible tiles. Unconventional Computing. To appear, 2005.
18. N. Jonoska, P. Sa-Ardyen, and N.C. Seeman. Genetic programming and evolvable machines. Computation by Self-assembly of DNA Graphs, 4.
19. M. Kao and R. Schweller. Reduce complexity for tile self-assembly through temperature programming. In Proceedings of 17th annual ACM-SIAM Symposium on Discrete Algorithms (SODA). To appear. ACM Press, 2006.
20. E. Klavins. Toward the control of self-assembling systems. In Control Problems in Robotics, volume 4, pages 153-168. Springer Verlag, 2002.
21. E. Klavins. Directed self-assembly using graph grammars. In Foundations of Nanoscience: Self Assembled Architectures and Devices, Snowbird, UT, 2004.
22. E. Klavins, R. Christ, and D. Lipsky. Graph grammars for self-assembling robotic systems. In Proceedings of the International Conference on Robotics and Automation, 2004.
23. T.H. LaBean, H. Yan, J. Kopatsch, F. Liu, E. Winfree, J.H. Reif, and N.C. Seeman. The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc., 122:1848-1860, 2000.
24. D. Lichtenstein. Planar formulae and their uses. SIAM J. Comput., 11(2):329-343, 1982.
25. J. Malo, J.C. Mitchell, C. Venien-Bryan, J.R. Harris, H. Wille, D.J. Sherratt, and A.J. Turberfield. Engineering a 2D protein-DNA crystal. Angew. Chem. Intl. Ed., 44:3057-3061, 2005.
26. C.M. Papadimitriou. Computational complexity. Addison-Wesley Publishing Company, Inc., 1st edition, 1994.
27. J.H. Reif, S. Sahu, and P. Yin. Compact error-resilient computational DNA tiling assemblies. In Proc. 10th International Meeting on DNA Computing, pages 248-260, 2004.
28. R.M. Robinson. Undecidability and non periodicity of tilings of the plane. Inventiones Math, 12:177-209, 1971.
29. P.W.K. Rothemund. Using lateral capillary forces to compute by self-assembly. Proc. Natl. Acad. Sci. USA, 97(3):984-989, 2000.
30. P.W.K. Rothemund, N. Papadakis, and E. Winfree. Algorithmic self-assembly of DNA sierpinski triangles. PLoS Biology 2 (12), 2:e424, 2004.
31. P.W.K. Rothemund and E. Winfree. The program-size complexity of self-assembled squares (extended abstract). In Proceedings of the thirty-second annual ACM symposium on Theory of computing, pages 459-468. ACM Press, 2000.
32. P. Sa-Ardyen, N. Jonoska, and N.C. Seeman. Self-assembling DNA graphs. Lecture Notes in Computer Science, 2568:1-9, 2003.
33. S. Sahu, P. Yin, and J.H. Reif. A self assembly model of time-dependent glue strength. In Proc. 11th International Meeting on DNA Computing, pages 113-124, 2005.
34. R. Schulman, S. Lee, N. Papadakis, and E. Winfree. One dimensional boundaries for DNA tile self-assembly. In DNA Based Computers 9, volume 2943 of LNCS, pages 108-125, 2004.
35. R. Schulman and E. Winfree. Programmable control of nucleation for algorithmic self-assembly. In DNA Based Computers 10, LNCS, 2005.
36. R. Schulman and E. Winfree. Self-replication and evolution of DNA crystals. In The 13th European Conference on Artificial Life (ECAL), 2005.
37. D. Soloveichik and E. Winfree. Complexity of compact proofreading for self-assembled patterns. In Proc. 11th International Meeting on DNA Computing, pages 125-135, 2005.
38. D. Soloveichik and E. Winfree. Complexity of self-assembled shapes. In DNA Based Computers 10, LNCS, 2005.
39. A. Strasser, L. O'Connor, and V.M. Dixit. Apoptosis signaling. Annu. Rev. Biochem., 69:217-245, 2000.
40. H. Wang. Proving theorems by pattern recognition ii. Bell Systems Technical Journal, 40: 1-41, 1961.
41. E. Winfree. Self-healing tile sets. Draft, 2005.
42. E. Winfree and R. Bekbolatov. Proofreading tile sets: Error correction for algorithmic self-assembly. In DNA Based Computers 9, volume 2943 of LNCS, pages 126-144, 2004.
43. E. Winfree, F. Liu, L.A. Wenzler, and N.C. Seeman. Design and self-assembly of two-dimensional DNA crystals. Nature, 394(6693):539-544, 1998.
44. H. Yan, T.H. LaBean, L. Feng, and J.H. Reif. Directed nucleation assembly of DNA tile complexes for barcode patterned DNA lattices. Proc. Natl. Acad. Sci. USA, 100(14): 8103-8108, 2003.