A Minimal Requirement for Self-assembly of Lines in Polylogarithmic Time

Self-assembly is the process in which small and simple components assemble into large and complex structures without explicit external control. The nubot model generalizes previous self-assembly models (e.g. aTAM) to include active components which can actively move and undergo state changes. One main difference between the nubot model and previous self-assembly models is its ability to perform exponential growth.

[1]  Robert M. Dirks,et al.  An autonomous polymerization motor powered by DNA hybridization , 2007, Nature Nanotechnology.

[2]  Erik Winfree,et al.  Complexity of Self-Assembled Shapes , 2004, SIAM J. Comput..

[3]  N. Pierce,et al.  A synthetic DNA walker for molecular transport. , 2004, Journal of the American Chemical Society.

[4]  Erik Winfree,et al.  Two computational primitives for algorithmic self-assembly: copying and counting. , 2005, Nano letters.

[5]  Sudheer Sahu,et al.  Autonomous Programmable Nanorobotic Devices Using DNAzymes , 2007, DNA.

[6]  Ashish Goel,et al.  Running time and program size for self-assembled squares , 2001, STOC '01.

[7]  Ming-Yang Kao,et al.  Reducing tile complexity for self-assembly through temperature programming , 2006, SODA '06.

[8]  G. Seelig,et al.  Enzyme-Free Nucleic Acid Logic Circuits , 2022 .

[9]  David Doty,et al.  Randomized Self-Assembly for Exact Shapes , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[10]  Ho-Lin Chen,et al.  Fast Algorithmic Self-assembly of Simple Shapes Using Random Agitation , 2014, DNA.

[11]  A. Turberfield,et al.  Coordinated chemomechanical cycles: a mechanism for autonomous molecular motion. , 2008, Physical review letters.

[12]  M. Win,et al.  Higher-Order Cellular Information Processing with Synthetic RNA Devices , 2008, Science.

[13]  E. Winfree,et al.  Algorithmic Self-Assembly of DNA Sierpinski Triangles , 2004, PLoS biology.

[14]  N. Seeman,et al.  Construction of a DNA-Truncated Octahedron , 1994 .

[15]  Erik Winfree,et al.  The program-size complexity of self-assembled squares (extended abstract) , 2000, STOC '00.

[16]  Robert M. Dirks,et al.  Triggered amplification by hybridization chain reaction. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[17]  N. Seeman,et al.  DNA double-crossover molecules. , 1993, Biochemistry.

[18]  N. Seeman,et al.  A precisely controlled DNA biped walking device , 2004 .

[19]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[20]  E. Klavins,et al.  An improved autonomous DNA nanomotor. , 2007, Nano letters.

[21]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[22]  P. Yin,et al.  A DNAzyme that walks processively and autonomously along a one-dimensional track. , 2005, Angewandte Chemie.

[23]  Erik Winfree,et al.  Active self-assembly of algorithmic shapes and patterns in polylogarithmic time , 2013, ITCS '13.

[24]  Michail G. Lagoudakis,et al.  2D DNA self-assembly for satisfiability , 1999, DNA Based Computers.

[25]  A. Turberfield,et al.  A DNA-fuelled molecular machine made of DNA , 2022 .

[26]  John H. Reif,et al.  Designs of Autonomous Unidirectional Walking DNA Devices , 2004, DNA.

[27]  D. Y. Zhang,et al.  Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA , 2007, Science.

[28]  Shawn M. Douglas,et al.  Self-assembly of DNA into nanoscale three-dimensional shapes , 2009, Nature.

[29]  Erik Winfree,et al.  Reducing facet nucleation during algorithmic self-assembly. , 2007, Nano letters.

[30]  Harry M. T. Choi,et al.  Programming biomolecular self-assembly pathways , 2008, Nature.

[31]  William M. Shih,et al.  A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron , 2004, Nature.

[32]  N. Seeman,et al.  Operation of a DNA Robot Arm Inserted into a 2D DNA Crystalline Substrate , 2006, Science.

[33]  Shawn M. Douglas,et al.  Folding DNA into Twisted and Curved Nanoscale Shapes , 2009, Science.

[34]  P. Rothemund Folding DNA to create nanoscale shapes and patterns , 2006, Nature.