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
Parallelism and time in hierarchical self-assembly
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Self-assembly with geometric tiles
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The two-handed tile assembly model is not intrinsically universal
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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.