Self-healing Tile Sets

L.M. Adleman, Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, November 11, 1994.Google Scholar

L.M. Adleman, Q. Cheng, A. Goel, M.-D.A. Huang, Running time and program size for self-assembled squares. In ACM Symposium on Theory of Computing (STOC), pages 740–748, 2001.Google Scholar

G. Aggarwal, Q. Cheng, M.H. Goldwasser, M.-Y. Kao, P.M. de Espanes, R.T. Schweller, Complexities for generalized models of self-assembly. SIAM Journal on Computing, 34:1493–1515, 2005.MathSciNetCrossRefGoogle Scholar

A.G. Cairns-Smith. The Life Puzzle: on Crystals and Organisms and on the Possibility of a Crystal as an Ancestor. Oliver and Boyd, New York, 1971.Google Scholar

H.-L. Chen, A. Goel, Error free self-assembly using error prone tiles. In Ferretti et al. eds. DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, pages 62–75, 2005.Google Scholar

H.-L. Chen, Q. Cheng, A. Goel, M. deh Huang, P.M. de Espanés, Invadable self-assembly: Combining robustness with efficiency. ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 883–892, 2004.Google Scholar

Q. Cheng, P.M. de Espanes, Resolving two open problems in the self-assembly of squares. Computer science technical report #03-793, University of Southern California, 2003.Google Scholar

C. Ferretti, G. Mauri, C. Zandron, eds., DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, 2005.Google Scholar

T-J. Fu, N.C. Seeman, DNA double-crossover molecules. Biochemistry, 32:3211–3220, 1993.CrossRefGoogle Scholar

K. Fujibayashi, S. Murata, A method of error suppression for self-assembling DNA tiles. In Ferretti et al. eds. DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, pages 113–127, 2005.Google Scholar

A.L. Mackay. Generalised crystallography. Izvj. Jugosl. Centr. Krist. (Zagreb), 10:15–36, 1975.Google Scholar

K. Morita, Computation-universality of one-dimensional one-way reversible cellular automata. Information Processing Letters, 42:325–329, 1992.zbMATHMathSciNetCrossRefGoogle Scholar

C. Radin, Tiling, periodicity, and crystals. J. Math. Phys., 26(6):1342–1344, 1985.MathSciNetCrossRefGoogle Scholar

J.H. Reif, S. Sahu, P. Yin, Compact error-resilient computational DNA tiling assemblies. In Ferretti et al. eds. DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, pages 293–307, 2005.Google Scholar

B.H. Robinson, N.C. Seeman, The design of a biochip: A self-assembling molecular-scale memory device. Protein Engineering, 1(4):295–300, 1987.Google Scholar

P.W.K. Rothemund, E. Winfree, The program-size complexity of self-assembled squares. In Symposium on Theory of Computing (STOC), ACM, 2000.Google Scholar

R. Schulman, E. Winfree, Programmable control of nucleation for algorithmic self-assembly. In Ferretti et al. eds. DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, pages 319–328, 2005.Google Scholar

R. Schulman, E. Winfree. Self-replication and evolution of DNA crystals. To appear in the proceedings of the VIII^thEuropean Conference on Artificial Life (ECAL).Google Scholar

N. C. Seeman, Nucleic-acid junctions and lattices. Journal of Theoretical Biology, 99(2):237–247, 1982.CrossRefGoogle Scholar

N.C. Seeman, P.S. Lukeman, Nucleic acid nanostructures: bottom-up control of geometry on the nanoscale. Reports on Progress in Physics, 68:237–270, 2005.CrossRefGoogle Scholar

D. Soloveichik, E. Winfree, Complexity of self-assembled shapes. In Ferretti et al. eds. DNA Computing 10, volume LNCS 3384, Berlin Heidelberg, Springer-Verlag, pages 344–354, 2005. Extended abstract; preprint of the full paper is cs.CC/0412096 on arXiv.org.Google Scholar

D. Soloveichik, E. Winfree, Complexity of compact proofreading for self-assembled patterns. Extended abstract. in Proceedings of the 11th Meeting on DNA Based Computing, London, Canada, Springer, LNCS 2005 (to appear).Google Scholar

A.J. Turberfield, B. Yurke, A.P. Mills, Jr., DNA hybridization catalysts and molecular tweezers. In Erik Winfree and David K. Gifford, editors, DNA Based Computers V, volume 54 of DIMACS, American Mathematical Society, Providence, RI, 2000.Google Scholar

H. Wang, An unsolvable problem on dominoes. Technical Report BL-30 (II-15), Harvard Computation Laboratory, 1962.Google Scholar

E. Winfree, F. Liu, L.A. Wenzler, N.C. Seeman, Design and self-assembly of two-dimensional DNA crystals. Nature, 394:539–544, 1998.CrossRefGoogle Scholar

E. Winfree, On the computational power of DNA annealing and ligation. In Richard J. Lipton and Eric B. Baum, editors, DNA Based Computers, volume 27 of DIMACS, American Mathematical Society, Providence, RI, pages 199–221, 1996.Google Scholar

E. Winfree, R. Bekbolatov, Proofreading tile sets: Error-correction for algorithmic self-assembly. In Junghuei Chen and John Reif, editors, DNA Computing 9, volume LNCS 2943, Springer-Verlag, Berlin Heidelberg, pages 126–144, 2004.Google Scholar

E. Winfree, Simulations of computing by self-assembly. Technical Report CSTR:1998.22, Caltech, 1998.Google Scholar

E. Winfree, Algorithmic self-assembly of DNA: Theoretical motivations and 2D assembly experiments. Journal of Biomolecular Structure & Dynamics, pages 263–270, 2000. Special issue S2.Google Scholar