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
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity of compact proofreading for self-assembled patterns
DNA'05 Proceedings of the 11th international conference on DNA Computing
Proceedings of the 10th international conference on DNA computing
DNA'04 Proceedings of the 10th 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
A molecular solution to the hitting-set problem in DNA-based supercomputing
Information Sciences: an International Journal
Polyomino-safe DNA self-assembly via block replacement
Natural Computing: an international journal
Optimizing tile concentrations to minimize errors and time for DNA tile self-assembly systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Theory of algorithmic self-assembly
Communications of the ACM
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DNA self-assembly has emerged as a rich and promising primitive for nano-technology. Experimental and analytical evidence indicates that such systems are prone to errors, and accordingly, several error-correction mechanisms have been proposed for the tile model of self-assembly. These error-correction mechanisms suffer either from high resolution loss or a large increase in the number of tile-types. In this paper, we propose dimension augmented proof-reading, a technique that uses the third dimension to do error-correction in two dimensional self-assembling systems. This involves no resolution loss in the two dimensions of interest, results in a smaller increase in the number of tile-types than previous techniques, and appears to have the same error-correction properties. Error-correcting systems need to be analyzed in the kinetic Tile Assembly Model; such analysis involves complicated Markov Chains and is cumbersome. In this paper, we also present a set of completely combinatorial criteria that can be used to prove properties of error-correcting self-assembling systems. We illustrate these criteria by applying them to two known proof-reading systems, one of which was not previously known to work. We then use these criteria to prove the correctness of dimension augmented proof-reading applied to a self-assembling system that computes the parity of a string.