The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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
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
Computability and Complexity in Self-assembly
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Self-assembly of Decidable Sets
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
Error suppression mechanisms for DNA tile self-assembly and their simulation
Natural Computing: an international journal
Activatable tiles: compact, robust programmable assembly and other applications
DNA13'07 Proceedings of the 13th international conference on DNA computing
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
Complexity of compact proofreading for self-assembled patterns
DNA'05 Proceedings of the 11th international conference on DNA Computing
Design and simulation of self-repairing DNA lattices
DNA'06 Proceedings of the 12th international conference on DNA Computing
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
Negative interactions in irreversible self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
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We investigate methods for exploiting nondeterminism inherent within the Tile Assembly Model in order to generate uniform random numbers. Namely, given an integer range {0,...,n *** 1}, we exhibit methods for randomly selecting a number within that range. We present three constructions exhibiting a trade-off between space requirements and closeness to uniformity. The first selector selects a random number with probability ***(1/n ) using O (log2 n ) tiles. The second selector takes a user-specified parameter that guarantees the probabilities are arbitrarily close to uniform, at the cost of additional space. The third selector selects a random number with probability exactly 1/n , and uses no more space than the first selector with high probability, but uses potentially unbounded space.