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
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
DNA13'07 Proceedings of the 13th international conference on DNA computing
Complexity of compact proofreading for self-assembled patterns
DNA'05 Proceedings of the 11th international conference on DNA Computing
DNA'04 Proceedings of the 10th 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
Programmable control of nucleation for algorithmic self-assembly
DNA'04 Proceedings of the 10th international conference on DNA computing
| Hi-index | 0.00 |
The standard abstract model for analyzing DNA self-assembly, aTAM, assumes that single tiles attach one by one to a larger structure. In practice, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. Such polyominoes may cause errors in systems designed with only aTAM in mind. In this paper, we first present a formal definition of when one tile system is a "block replacement" of another. Then we present a block replacement scheme for making any system that admits non-trivial block replacement polyomino-safe. In addition, we present a smaller block replacement scheme that makes the Chinese Remainder counter polyomino-safe and prove that the question of whether a system is polyomino-safe (or other similar properties) is undecidable. Finally, we show that applying our polyomino-safe system produces self-healing systems when applied to most self-healing systems.