Computational complexity of loss networks
Theoretical Computer Science - Special issue on probabilistic modelling
Communications of the ACM
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
The emerging discipline of biomolecular computation in the US
New Generation Computing
Molecular Assembly and Computation: From Theory to Experimental Demonstrations
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Self assembly times in DNA-based computation
ACM SIGMETRICS Performance Evaluation Review
Arithmetic computation in the tile assembly model: Addition and multiplication
Theoretical Computer Science
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
Toward minimum size self-assembled counters
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
Solving satisfiability in the tile assembly model with a constant-size tileset
Journal of Algorithms
Complexity classes for self-assembling flexible tiles
Theoretical Computer Science
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
Path finding in the tile assembly model
Theoretical Computer Science
Pictures worth a thousand tiles, a geometrical programming language for self-assembly
Theoretical Computer Science
The 4-way deterministic tiling problem is undecidable
Theoretical Computer Science
Two lower bounds for self-assemblies at temperature 1
Proceedings of the 2009 ACM symposium on Applied Computing
Self-assembly of discrete self-similar fractals
Natural Computing: an international journal
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
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
Evolving physical self-assembling systems in two-dimensions
ICES'10 Proceedings of the 9th international conference on Evolvable systems: from biology to hardware
Self-assembly of infinite structures: A survey
Theoretical Computer Science
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
Synthesizing minimal tile sets for patterned DNA self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Complexity of graph self-assembly in accretive systems and self-destructible systems
Theoretical Computer Science
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
Natural Computing: an international journal
On stoichiometry for the assembly of flexible tile DNA complexes
Natural Computing: an international journal
Self-correcting self-assembly: growth models and the hammersley process
DNA'05 Proceedings of the 11th international conference on DNA Computing
Expectation and variance of self-assembled graph structures
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
A self-assembly model of time-dependent glue strength
DNA'05 Proceedings of the 11th international conference on DNA Computing
Parallelism and time in hierarchical self-assembly
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A critical view of the evolutionary design of self-assembling systems
EA'05 Proceedings of the 7th international conference on Artificial Evolution
A computational model for self-assembling flexible tiles
UC'05 Proceedings of the 4th international conference on Unconventional Computation
Spectrum of a pot for DNA complexes
DNA'06 Proceedings of the 12th 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
The power of nondeterminism in self-assembly
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Design, simulation, and experimental demonstration of self-assembled DNA nanostructures and motors
UPP'04 Proceedings of the 2004 international conference on Unconventional Programming Paradigms
DNA'04 Proceedings of the 10th international conference on DNA computing
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
Program size and temperature in self-assembly
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Natural Computing: an international journal
Efficient 3-SAT algorithms in the tile assembly model
Natural Computing: an international journal
On the behavior of tile assembly system at high temperatures
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Theory of algorithmic self-assembly
Communications of the ACM
Programming and evolving physical self-assembling systems in three dimensions
Natural Computing: an international journal
Step-wise tile assembly with a constant number of tile types
Natural Computing: an international journal
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly
Theoretical Computer Science
The two-handed tile assembly model is not intrinsically universal
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Exploring programmable self-assembly in non-DNA based molecular computing
Natural Computing: an international journal
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Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape.Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape.We prove that the first problem is NP-complete in general, and polynomial time solvable on trees and squares. In order to prove that the problem is in NP, we present a polynomial time algorithm to verify whether a given tile system uniquely produces a given shape. This algorithm is analogous to a program verifier for traditional computational systems, and may well be of independent interest. For the second problem, we present a polynomial time $O(\log n)$-approximation algorithm that works for a large class of tile systems that we call partial order systems.