Logical depth and physical complexity
A half-century survey on The Universal Turing Machine
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
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
Theory and experiments in algorithmic self-assembly
Theory and experiments in algorithmic self-assembly
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Computation with finite stochastic chemical reaction networks
Natural Computing: an international journal
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Randomized Self-Assembly for Exact Shapes
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Self-assemblying classes of shapes with a minimum number of tiles, and in optimal time
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
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
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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Working in Winfree's abstract tile assembly model, we show that a constant-sized tile assembly system can be programmed through relative tile concentrations to build an $n\times n$ square with high probability for any sufficiently large $n$. This answers an open question of Kao and Schweller [Automata, Languages and Programming, Lecture Notes in Comput. Sci. 5125, Springer, Berlin, 2008, pp. 370-384], who showed how to build an approximately $n\times n$ square using tile concentration programming and asked whether the approximation could be made exact with high probability. We show how this technique can be modified to answer another question of Kao and Schweller by showing that a constant-sized tile assembly system can be programmed through tile concentrations to assemble arbitrary finite scaled shapes, which are shapes modified by replacing each point with a $c\times c$ block of points for some integer $c$. Furthermore, we exhibit a smooth trade-off between specifying bits of $n$ via tile concentrations versus specifying them via hard-coded tile types, which allows tile concentration programming to be employed for specifying a fraction of the bits of “input” to a tile assembly system, under the constraint that concentrations can be specified to only a limited precision. Finally, to account for some unrealistic aspects of the tile concentration programming model, we show how to modify the construction to use only concentrations that are arbitrarily close to uniform.