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
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Complexities for Generalized Models of Self-Assembly
SIAM Journal on Computing
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
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
Solving satisfiability in the tile assembly model with a constant-size tileset
Journal of Algorithms
Path finding in the tile assembly model
Theoretical Computer Science
Efficient Algorithms for Self Assembling Triangular and Other Nano Structures
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
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
Shape replication through self-assembly and RNase enzymes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Triangular tile self-assembly systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Randomized self assembly of rectangular nano structures
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
Efficient algorithms for self assembling non-rectangular nano structures
Natural Computing: an international journal
Self-assembly of decidable sets
Natural Computing: an international journal
Polyominoes simulating arbitrary-neighborhood zippers and tilings
Theoretical Computer Science
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
Randomized Self-Assembly for Exact Shapes
SIAM Journal on 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
On the complexity of graph self-assembly in accretive systems
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
Triangular and hexagonal tile self-assembly systems
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Natural Computing: an international journal
Efficient 3-SAT algorithms in the tile assembly model
Natural Computing: an international journal
Theory of algorithmic self-assembly
Communications of the ACM
Programming and evolving physical self-assembling systems in three dimensions
Natural Computing: an international journal
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We consider the tile self-assembly model and how tile complexity can be eliminated by permitting the temperature of the self-assembly system to be adjusted throughout the assembly process. To do this, we propose novel techniques for designing tile sets that permit an arbitrary length m binary number to be encoded into a sequence of O(m) temperature changes such that the tile set uniquely assembles a supertile that precisely encodes the corresponding binary number. As an application, we show how this provides a general tile set of size O(1) that is capable of uniquely assembling essentially any n X n square, where the assembled square is determined by a temperature sequence of length O(log n) that encodes a binary description of n. This yields an important decrease in tile complexity from the required Ω(log n/log log n) for almost all n when the temperature of the system is fixed. We further show that for almost all n, no tile system can simultaneously achieve both o(log n) temperature complexity and O(log n/log log n) tile complexity, showing that both versions of an optimal square building scheme have been discovered. This work suggests that temperature change can constitute a natural, dynamic method for providing input to self-assembly systems that is potentially superior to the current technique of designing large tile sets with specific inputs hardwired into the tileset.