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
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Arithmetic computation in the tile assembly model: Addition and multiplication
Theoretical Computer Science
An Architectural Style for Solving Computationally Intensive Problems on Large Networks
SEAMS '07 Proceedings of the 2007 International Workshop on Software Engineering for Adaptive and Self-Managing Systems
Fault and adversary tolerance as an emergent property of distributed systems' software architectures
Proceedings of the 2007 workshop on Engineering fault tolerant systems
Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Nondeterministic polynomial time factoring in the tile assembly model
Theoretical Computer Science
Solving NP-complete problems in the tile assembly model
Theoretical Computer Science
Monomer Control for Error Tolerance in DNA Self-Assembly
Journal of Electronic Testing: Theory and Applications
On the complexity of graph self-assembly in accretive systems
Natural Computing: an international journal
Combining self-healing and proofreading in self-assembly
Natural Computing: an international journal
How crystals that sense and respond to their environments could evolve
Natural Computing: an international journal
Solving satisfiability in the tile assembly model with a constant-size tileset
Journal of Algorithms
Path finding in the tile assembly model
Theoretical Computer Science
Healing DNA Self-Assemblies Using Punctures
Journal of Electronic Testing: Theory and Applications
The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Random Number Selection in Self-assembly
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
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
Robust self-assembly of graphs
Natural Computing: an international journal
Describing self-assembly of nanostructures
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Activatable tiles: compact, robust programmable assembly and other applications
DNA13'07 Proceedings of the 13th international conference on DNA computing
Constant-size tileset for solving an NP-complete problem in nondeterministic linear time
DNA13'07 Proceedings of the 13th international conference on DNA computing
Controlling errors in the process of molecular self-assembly
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Proceedings of the Conference on Design, Automation and Test in Europe
Multiple error detection in DNA self-assembly using coded tiles
IEEE Transactions on Circuits and Systems II: Express Briefs
A coding framework for DNA self-assembly
NANOARCH '09 Proceedings of the 2009 IEEE/ACM International Symposium on Nanoscale Architectures
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
Programmable Control of Nucleation for Algorithmic Self-Assembly
SIAM Journal on Computing
The effect of malformed tiles on tile assemblies within the kinetic tile assembly model
Natural Computing: an international journal
Distributed agreement in tile self-assembly
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
Plane-filling properties of directed figures
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Randomized Self-Assembly for Exact Shapes
SIAM Journal on Computing
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
Complexity of compact proofreading for self-assembled patterns
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
Programmable control of nucleation for algorithmic self-assembly
DNA'04 Proceedings of the 10th international conference on DNA computing
Simple evolution of complex crystal species
Natural Computing: an international journal
Theory of algorithmic self-assembly
Communications of the ACM
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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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. We present an error-correction scheme, called snaked proof-reading, which can correct both growth and nucleation errors in a self-assembling system. This builds upon an earlier construction of Winfree and Bekbolatov [11], which could correct a limited class of growth errors. Like their construction, our system also replaces each tile in the system by a k × k block of tiles, and does not require changing the basic tile assembly model proposed by Rothemund and Winfree [8]. We perform a theoretical analysis of our system under fairly general assumptions: tiles can both attach and fall off depending on the thermodynamic rate parameters which also govern the error rate. We prove that with appropriate values of the block size, a seed row of n tiles can be extended into an n × n square of tiles without errors in expected time $\widetilde{O}(n)$, and further, this square remains stable for an expected time of $\widetilde{\Omega}(n)$. This is the first error-correction system for DNA self-assembly that has provably good assembly time (close to linear) and provable error-correction. The assembly time is thesame, up to logarithmic factors, as the time for an irreversible, error-free assembly. We also did a preliminary simulation study of our scheme. In simulations, our scheme performs much better (in terms of error-correction) than the earlier scheme of Winfree and Bekbolatov, and also much better than the unaltered tile system. Our basic construction (and analysis) applies to all rectilinear tile systems (where growth happens from south to north and west to east). These systems include the Sierpinski tile system, the square-completion tile system, and the block cellular automata for simulating Turing machines. It also applies to counters, a basic primitive in many self-assembly constructions and computations.