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
Theory and experiments in algorithmic self-assembly
Theory and experiments in algorithmic self-assembly
Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
International Journal of Mobile Network Design and Innovation
On the complexity of graph self-assembly in accretive systems
Natural Computing: an international journal
Toward minimum size self-assembled counters
Natural Computing: an international journal
Error suppression mechanisms for DNA tile self-assembly and their simulation
Natural Computing: an international journal
Polyomino-safe DNA self-assembly via block replacement
Natural Computing: an international journal
Toward minimum size self-assembled counters
DNA13'07 Proceedings of the 13th international conference on DNA computing
Complexity of graph self-assembly in accretive systems and self-destructible systems
Theoretical Computer Science
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
Natural Computing: an international journal
Beyond biology: designing a new mechanism for self-replication and evolution at the nanoscale
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Self-correcting self-assembly: growth models and the hammersley process
DNA'05 Proceedings of the 11th international conference on DNA Computing
Complexity of graph self-assembly in accretive systems and self-destructible systems
DNA'05 Proceedings of the 11th international conference on DNA Computing
A self-assembly model of time-dependent glue strength
DNA'05 Proceedings of the 11th international conference on DNA Computing
On the complexity of graph self-assembly in accretive systems
DNA'06 Proceedings of the 12th international conference on DNA Computing
DNA'06 Proceedings of the 12th international conference on DNA Computing
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
| Hi-index | 0.00 |
DNA self-assembly is emerging as a key paradigm for nano-technology, nano-computation, and several related disciplines. In nature, DNA self-assembly is often equipped with explicit mechanisms for both error prevention and error correction. For artificial self-assembly, these problems are even more important since we are interested in assembling large systems with great precision. So far, theoretical studies of DNA self-assembly have primarily focused on the efficiency of the assembly process in terms of the program size and the running time. In this paper, we perform a preliminary study of algorithms for DNA self-assembly that are both robust and efficient.Strand invasion is an important error-correction mechanism observed in several natural self-assembling systems. We first define invadable self-assemblies as self-assembling systems which can effectively use the strand invasion mechanism for error-correction. We then show that O(log2 n/ log log n) tiles are sufficient to assemble an n × n square in this model. The running time of our system is Õ (n). We obtain our result by growing a counter which simulates Chinese remaindering. The running time and the program size of our invadable system are within polylogarithmic factors of known lower bounds for general systems, i.e. the efficiency penalty for obtaining robustness is small in our model. We also show how to simulate an arbitrary Turing machine using an invadable self-assembly system.