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
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
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth 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
On the complexity of graph self-assembly in accretive systems
Natural Computing: an international journal
How crystals that sense and respond to their environments could evolve
Natural Computing: an international journal
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
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
Transformations and Preservation of Self-assembly Dynamics through Homotheties
Language and Automata Theory and Applications
Pictures worth a thousand tiles, a geometrical programming language for self-assembly
Theoretical Computer Science
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
DNA13'07 Proceedings of the 13th international conference on DNA computing
One-dimensional staged self-assembly
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Complexity of graph self-assembly in accretive systems and self-destructible systems
DNA'05 Proceedings of the 11th international conference on DNA Computing
A self-assembly model of time-dependent glue strength
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
On times to compute shapes in 2d tile self-assembly
DNA'06 Proceedings of the 12th international conference on DNA Computing
DNA'06 Proceedings of the 12th international conference on DNA Computing
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
One-dimensional staged self-assembly
Natural Computing: an international journal
| Hi-index | 0.00 |
The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly “program,” a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest self-assembly program that builds a shape and the shape's descriptional (Kolmogorov) complexity should be related. We show that under the notion of a shape that is independent of scale this is indeed so: in the Tile Assembly Model, the minimal number of distinct tile types necessary to self-assemble an arbitrarily scaled shape can be bounded both above and below in terms of the shape's Kolmogorov complexity. As part of the proof of the main result, we sketch a general method for converting a program outputting a shape as a list of locations into a set of tile types that self-assembles into a scaled up version of that shape. Our result implies, somewhat counter-intuitively, that self-assembly of a scaled up version of a shape often requires fewer tile types, and suggests that the independence of scale in self-assembly theory plays the same crucial role as the independence of running time in the theory of computability.