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
Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of Self-Assembled Shapes
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
Combining self-healing and proofreading in self-assembly
Natural Computing: an international journal
Randomized Self-Assembly for Exact Shapes
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Self-replication and evolution of DNA crystals
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
Programmable control of nucleation for algorithmic self-assembly
DNA'04 Proceedings of the 10th international conference on DNA computing
Graph-theoretic formalization of hybridization in DNA sticker complexes
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Graph-theoretic formalization of hybridization in DNA sticker complexes
Natural Computing: an international journal
| Hi-index | 0.00 |
DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile concentrations is easy to implement in actual lab experiments. We prove that setting the concentration of tile Ti proportional to the square root of Ni where Ni is the number of times Ti appears outside the seed structure in the final assembled shape minimizes the rate of growth errors for rectilinear tile systems. We also show that the same concentrations minimize the expected assembly time for a feasible class of tile systems. Moreover, for general tile systems, given tile concentrations, we can approximate the expected assembly time with high accuracy and probability by running only a polynomial number of simulations in the size of the target shape.