An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Complexities for Generalized Models of Self-Assembly
SIAM Journal on Computing
Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Solving NP-complete problems in the tile assembly model
Theoretical Computer Science
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Two lower bounds for self-assemblies at temperature 1
Proceedings of the 2009 ACM symposium on Applied Computing
The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Randomized Self-Assembly for Exact Shapes
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
DNA13'07 Proceedings of the 13th international conference on DNA computing
Activatable tiles: compact, robust programmable assembly and other applications
DNA13'07 Proceedings of the 13th international conference on DNA computing
Shape replication through self-assembly and RNase enzymes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Self-replication and evolution of DNA crystals
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
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
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
Programming and evolving physical self-assembling systems in three dimensions
Natural Computing: an international journal
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
| Hi-index | 0.02 |
We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no temperature 1 assembly system has been shown to build a shape with a tile complexity smaller than the diameter of the shape. In contrast, we show that temperature 1 self-assembly in 3 dimensions, even when growth is restricted to at most 1 step into the third dimension, is capable of simulating a large class of temperature 2 systems, in turn permitting the simulation of arbitrary Turing machines and the assembly of n x n squares in near optimal O(log n) tile complexity. Further, we consider temperature 1 probabilistic assembly in 2D, and show that with a logarithmic scale up of tile complexity and shape scale, the same general class of temperature τ = 2 systems can be simulated, yielding Turing machine simulation and O(log2 n) assembly of n x n squares with high probability. Our results show a sharp contrast in achievable tile complexity at temperature 1 if either growth into the third dimension or a small probability of error are permitted. Motivated by applications in nanotechnology and molecular computing, and the plausibility of implementing 3 dimensional self-assembly systems, our techniques may provide the needed power of temperature 2 systems, while at the same time avoiding the experimental challenges faced by those systems.