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
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
A Limit to the Power of Multiple Nucleation in Self-assembly
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Randomized fast design of short DNA words
ACM Transactions on Algorithms (TALG)
Self-assembly of discrete self-similar fractals
Natural Computing: an international journal
Toward minimum size self-assembled counters
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
Complexity of graph self-assembly in accretive systems and self-destructible systems
Theoretical Computer Science
Programmable Control of Nucleation for Algorithmic Self-Assembly
SIAM Journal on 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 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
Complexity of compact proofreading for self-assembled patterns
DNA'05 Proceedings of the 11th international conference on DNA Computing
Randomized fast design of short DNA words
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the complexity of graph self-assembly in accretive systems
DNA'06 Proceedings of the 12th international conference on DNA Computing
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
Flexible word design and graph labeling
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Self-assembly with geometric tiles
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Turing patterns with Turing machines: emergence and low-level structure formation
Natural Computing: an international journal
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In this paper, we extend Rothemund and Winfree's examination of the tile complexity of tile self-assembly [6]. They provided a lower bound of Ω(log N/log log N) on the tile complexity of assembling an N × N square for almost all N. Adleman et al. [1] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size O(√log N) which assembles an N × N square in a model which allows flexible glue strength between non-equal glues (This was independently discovered in [3]). This result is matched by a lower bound dictated by Kolmogorov complexity. For three other generalizations, we show that the Ω(log N/log log N) lower bound applies to N × N squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length N and width k, we provide a tighter lower bound of Ω(N(1/k)/k) for the standard model, yet we also give a construction which achieves O(log N/log log N) complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape, and show that this problem is NP-hard.