SIAM Journal on Computing
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
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
Strict Self-assembly of Discrete Sierpinski Triangles
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Computability and Complexity in Self-assembly
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Self-assembly of Decidable Sets
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Distributed agreement in tile self-assembly
Natural Computing: an international journal
ACM Computing Surveys (CSUR)
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Majumder, Reif and Sahu presented in [7] a model of reversible, error-permitting tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time. One open question they asked was how the model would change if it permitted multiple nucleation, i.e.,independent groups of tiles growing before attaching to the original seed assembly. This paper provides a partial answer, by proving that no tile assembly model can use multiple nucleation to achieve speedup from polynomial time to constant time without sacrificing computational power: if a tile assembly system $\mathcal{T}$ uses multiple nucleation to tile a surface in constant time (independent of the size of the surface), then $\mathcal{T}$ is unable to solve computational problems that have low complexity in the (single-seeded) Winfree-Rothemund Tile Assembly Model. The proof technique defines a new model of distributed computing that simulates tile assembly, so a tile assembly model can be described as a distributed computing model.