Combining self-healing and proofreading in self-assembly
Natural Computing: an international journal
Computability and Complexity in Self-assembly
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Self-assembly of Decidable Sets
UC '08 Proceedings of the 7th international conference on Unconventional Computing
A Limit to the Power of Multiple Nucleation in Self-assembly
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Solving satisfiability in the tile assembly model with a constant-size tileset
Journal of Algorithms
Complexity classes for self-assembling flexible tiles
Theoretical Computer Science
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
Two lower bounds for self-assemblies at temperature 1
Proceedings of the 2009 ACM symposium on Applied Computing
Efficient Algorithms for Self Assembling Triangular and Other Nano Structures
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Brief announcement: self-assembly as graph grammar as distributed system
Proceedings of the 28th ACM symposium on Principles of distributed computing
Random Number Selection in Self-assembly
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
Error suppression mechanisms for DNA tile self-assembly and their simulation
Natural Computing: an international journal
Self-assembly of discrete self-similar fractals
Natural Computing: an international journal
Activatable tiles: compact, robust programmable assembly and other applications
DNA13'07 Proceedings of the 13th international conference on DNA computing
Approximate self-assembly of the Sierpinski triangle
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Self-assembly of infinite structures: A survey
Theoretical Computer Science
Improving efficiency of 3-SAT-solving tile systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Optimizing tile concentrations to minimize errors and time for DNA tile self-assembly systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Programmable Control of Nucleation for Algorithmic Self-Assembly
SIAM Journal on Computing
On aggregation in multiset-based self-assembly of graphs
Natural Computing: an international journal
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
Natural Computing: an international journal
Distributed agreement in tile self-assembly
Natural Computing: an international journal
Efficient algorithms for self assembling non-rectangular nano structures
Natural Computing: an international journal
Self-assembly of decidable sets
Natural Computing: an international journal
Self-assembling rulers for approximating generalized sierpinski carpets
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Exact shapes and turing universality at temperature 1 with a single negative glue
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Information content of colored motifs in complex networks
Artificial Life
Randomized Self-Assembly for Exact Shapes
SIAM Journal on Computing
Parallelism and time in hierarchical self-assembly
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A computational model for self-assembling flexible tiles
UC'05 Proceedings of the 4th international conference on Unconventional Computation
The power of nondeterminism in self-assembly
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Natural Computing: an international journal
Efficient 3-SAT algorithms in the tile assembly model
Natural Computing: an international journal
Self-assembly with geometric tiles
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Theory of algorithmic self-assembly
Communications of the ACM
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly “program,” a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest self-assembly program that builds a shape and the shape’s descriptional (Kolmogorov) complexity should be related. We show that when using a notion of a shape that is independent of scale, this is indeed so: in the tile assembly model, the minimal number of distinct tile types necessary to self-assemble a shape, at some scale, can be bounded both above and below in terms of the shape’s Kolmogorov complexity. As part of the proof, we develop a universal constructor for this model of self-assembly that can execute an arbitrary Turing machine program specifying how to grow a shape. Our result implies, somewhat counterintuitively, that self-assembly of a scaled-up version of a shape often requires fewer tile types. Furthermore, the independence of scale in self-assembly theory appears to play the same crucial role as the independence of running time in the theory of computability. This leads to an elegant formulation of languages of shapes generated by self-assembly. Considering functions from bit strings to shapes, we show that the running-time complexity, with respect to Turing machines, is polynomially equivalent to the scale complexity of the same function implemented via self-assembly by a finite set of tile types. Our results also hold for shapes defined by Wang tiling—where there is no sense of a self-assembly process—except that here time complexity must be measured with respect to nondeterministic Turing machines.