Non-cooperatively Assembling Large Structures

Algorithmic self-assembly is the study of the local, distributed, asynchronous algorithms ran by molecules to self-organise, in particular during crystal growth. The general cooperative model, also called “temperature 2”, uses synchronisation to simulate Turing machines, build shapes using the smallest possible amount of tile types, and other algorithmic tasks. However, in the non-cooperative (“temperature 1”) model, the growth process is entirely asynchronous, and mostly relies on geometry. Even though the model looks like a generalisation of finite automata to two dimensions, its 3D generalisation is capable of performing arbitrary (Turing) computation [SODA 2011], and of universal simulations [SODA 2014], whereby a single 3D non-cooperative tileset can simulate the dynamics of all possible 3D non-cooperative systems, up to a constant scaling factor.

[1]  E. Winfree.  Simulations of Computing by Self-Assembly , 1998 .

[2]  Erik D. Demaine,et al.  Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM , 2013, STACS.

[3]  Erik D. Demaine,et al.  One Tile to Rule Them All: Simulating Any Tile Assembly System with a Single Universal Tile , 2014, ICALP.

[4]  Pierre-Etienne Meunier,et al.  The non-cooperative tile assembly model is not intrinsically universal or capable of bounded Turing machine simulation , 2017, STOC.

[5]  Jacob Hendricks,et al.  The Power of Duples (in Self-Assembly): It's Not So Hip to Be Square , 2014, COCOON.

[6]  Ján Manuch,et al.  Two Lower Bounds for Self-Assemblies at Temperature 1 , 2010, J. Comput. Biol..

[7]  Robert T. Schweller,et al.  Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D , 2009, SODA '11.

[8]  Matthew J. Patitz,et al.  Asynchronous signal Passing for Tile Self-assembly: Fuel Efficient Computation and Efficient assembly of Shapes , 2012, Int. J. Found. Comput. Sci..

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

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

[11]  Wei Li,et al.  A cargo-sorting DNA robot , 2017, Science.

[12]  Matthew J. Patitz,et al.  Intrinsic universality in tile self-assembly requires cooperation , 2013, SODA.

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

[14]  Sándor P. Fekete,et al.  Universal Computation with Arbitrary Polyomino Tiles in Non-Cooperative Self-Assembly , 2014, SODA.

[15]  Leonard M. Adleman,et al.  Theory and experiments in algorithmic self-assembly , 2001 .

[16]  Matthew J. Patitz,et al.  Exact Shapes and Turing Universality at Temperature 1 with a Single Negative Glue , 2011, DNA.

[17]  Jack H. Lutz,et al.  The Tile Assembly Model is Intrinsically Universal , 2011, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

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

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

[20]  Matthew J. Patitz,et al.  Limitations of self-assembly at temperature 1 , 2009, Theor. Comput. Sci..

[21]  Jacob Hendricks,et al.  Computing in continuous space with self-assembling polygonal tiles (extended abstract) , 2015, SODA.