The program-size complexity of self-assembled squares (extended abstract)

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2000, Pages 459-468

  Rothemund, Paul W K ^a   Winfree, Erik ^b  

^a University of Southern California   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABLE FUNCTIONS; COOPERATIVE BONDING; EXTENDED ABSTRACTS; INTERACTION STRENGTH; MOLECULAR SELF ASSEMBLY; POINT OF VIEWS; PROGRAM-SIZE COMPLEXITY; TILE ASSEMBLY MODELS; SELF-ASSEMBLED SQUARES; TILE ASSEMBLY MODEL;

SELF ASSEMBLY; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS;

COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY;

EID: 0033701726     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/335305.335358     Document Type: Conference Paper

References (27)

1. Adleman, L. M. (1994). Molecular computation of solutions to combinatorial problems. Science, 266:1021-1024.
2. Adleman, L. M. (unpublished manuscript, 2000). Toward a mathematical theory of self-assembly.
3. Bennett, C. H. (1982). The thermodynamics of computation - a review. International Journal of Theoretical Physics, 21(12):905-940.
4. Berger, R. (1966). The undecidability of the domino problem. Memiors of the AMS, 66:1-72.
5. Bowden, N., Choi, I., Gryzbowski, B., and Whitesides, G. (1999). Mesoscale self-assembly of hexagonal plates using lateral capillary forces: Synthesis using the "capillary bond". Journal of the American Chemical Society, 121:5373-5391.
6. Bowden, N., Terfort, A., Carbeck, J., and Whitesides, G. (1997). Self-assembly of mesoscale objects into ordered two-dimensional arrays. Science, 276:233-235. (Pubitemid 27172675)
7. Hjelmfelt, A. and Ross, J. (1995). Implementation of logic functions and computations by chemical kinetics. Physica D, 84:180-193.
8. Hosokawa, K., Shimoyama, I., and Miura, H. (1996). Two-dimensional micro-self-assembly using the surface tension of water. Sensors and Actuators A, 57:117-125. (Pubitemid 126371391)
9. Kurtz, S. A., Mahaney, S. R., Royer, J. S., and Simon, J. (1997). Biological computing. In Hemaspaandra, L. A. and Selman, A. L., editors, Complexity Theory Retrospective II, pages 179-195. Springer.
10. Li, M. and Vitanyi, P. (1997). An Introduction to Kolmogorov Complexity and Its Applications (Second Edition). Springer Verlag, New York.
11. Mackay, A. (1995). Generalised crystallography. Journal of Molecular Structure (Theochem), 336:293-303.
12. Magnasco, M. O. (1997). Chemical kinetics is Turing universal. Physical Review Letters, 78(6):1190-1193.
13. Markov, I. V. (1995). Crystal Growth for Beginners: fundamentals of nucleation, crystal growth, and epitaxy. World Scientific, Singapore.
14. Ptashne, M. (1992). A Genetic Switch, 2nd ed. Cell Press & Blackwell.
15. Radin, C. (1991). Global order from local sources. Bulletin of the AMS, 25(2):335-364.
16. Rado, T. (1962). On non-computable functions. Bell System Technical Journal, 41(3):877-884.
17. Robinson, R. M. (1971). Undecidability and nonperiodicity of tilings of the plane. Inventiones Math., 12:177-209.
18. Rothemund, P. W. K. (2000). Using lateral capillary forces to compute by self-assembly. Proceedings of the National Academy of Sciences, 97:984-989.
19. Schectman, D., Blech, I., Gratias, D., and Cahn, J. (1984). Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett., 53:1951-1953.
20. Seeman, N. C. (1998). DNA nanotechnology: novel DNA constructions. Annual Review of Biophysics and Biomolecular Structure, 27:225-248.
21. Senechal, M. (1995). Quasicrystals and geometry. Cambridge University Press, Cambridge.
22. Wang, H. (1961). Proving theorems by pattern recognition. II. Bell System Technical Journal, 40:1-42.
23. Wang, H. (1963). Dominoes and the AEA case of the decision problem. In Fox, J., editor, Mathematical Theory of Automata, pages 23-55, Brooklyn, New York. Polytechnic Press.
24. Winfree, E. (1996). On the computational power of DNA annealing and ligation. In Lipton, R. J. and Baum, E. B., editors, DNA Based Computers: DIMACS Workshop, April 4, 1995, volume 27, pages 199-221, Providence, RI. American Mathematical Society.
25. th DIMACS Meeting on DNA Based Computers, held at the University of Pennsylvania, June 16-19, 1998.
26. Winfree, E., Liu, F., Wenzler, L. A., and Seeman, N. C. (1998a). Design and self-assembly of two-dimensional DNA crystals. Nature, 394:539-544. (Pubitemid 28366820)
27. Winfree, E., Yang, X., and Seeman, N. C. (1998b). Universal computation via self-assembly of DNA: Some theory and experiments. In Landweber, L. F. and Baum, E. B., editors, DNA Based Computers II: DIMACS Workshop, June 10-12, 1996, volume 44, Providence, RI. American Mathematical Society.