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
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A Framework for Designing Novel Magnetic Tiles Capable of Complex Self-assemblies
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
The Undecidability of the Infinite Ribbon Problem: Implications for Computing by Self-Assembly
SIAM Journal on Computing
Polyomino-Safe DNA Self-assembly via Block Replacement
DNA Computing
Limitations of self-assembly at temperature 1
Theoretical Computer Science
Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Negative interactions in irreversible self-assembly
DNA'10 Proceedings of the 16th 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
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
Theory of algorithmic self-assembly
Communications of the ACM
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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Is Winfree's abstract Tile Assembly Model (aTAM) "powerful?" Well, if certain tiles are required to "cooperate" in order to be able to bind to a growing tile assembly (a.k.a., temperature 2 self-assembly), then Turing universal computation and the efficient self-assembly of N × N squares is achievable in the aTAM (Rotemund and Winfree, STOC 2000). So yes, in a computational sense, the aTAM is quite powerful! However, if one completely removes this cooperativity condition (a.k.a., temperature 1 self-assembly), then the computational "power" of the aTAM (i.e., its ability to support Turing universal computation and the efficient self-assembly of N × N squares) becomes unknown. On the plus side, the aTAM, at temperature 1, is not only Turing universal but also supports the efficient self-assembly N × N squares if self-assembly is allowed to utilize three spatial dimensions (Fu, Schweller and Cook, SODA 2011). In this paper, we investigate the theoretical "power" of a seemingly simple, restrictive variant of Winfree's aTAM in which (1) the absolute value of every glue strength is 1, (2) there is a single negative strength glue type and (3) unequal glues cannot interact (i.e., glue functions must be "diagonal"). We call this abstract model of self-assembly the restricted glue Tile Assembly Model (rgTAM). We achieve two positive results. First, we show that the tile complexity of uniquely producing an N × N square in the rgTAM is O(log N). In our second result, we prove that the rgTAM is Turing universal.