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
Elements of the Theory of Computation
Elements of the Theory of Computation
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
SIAM Journal on Computing
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
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
Computational Complexity: A Modern Approach
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The Tile Complexity of Linear Assemblies
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Step-Assembly with a Constant Number of Tile Types
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Randomized Self-Assembly for Exact Shapes
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Shape replication through self-assembly and RNase enzymes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Limitations of self-assembly at temperature 1
Theoretical Computer Science
Negative interactions in irreversible self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Computability and Complexity in Self-assembly
Theory of Computing Systems
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
Parallelism and time in hierarchical self-assembly
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
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We investigate the role of nondeterminism in Winfree's abstract tile assembly model, which was conceived to model artificial molecular self-assembling systems constructed from DNA. By nondeterminism we do not mean a magical ability such as that possessed by a nondeterministic algorithm to search an exponential-size space in polynomial time. Rather, we study realistically implementable systems that retain a different sense of determinism in that they are guaranteed to produce a unique shape but are nondeterministic in that they do not guarantee which tile types will be placed where within the shape. We show a "molecular computability" result: there is an infinite shape S that is uniquely assembled by a tile system but not by any deterministic tile system. We show a "molecular complexity" result: there is a finite shape S that is uniquely assembled by a tile system with c tile types, but every deterministic tile system that uniquely assembles S has more than c tile types. In fact we extend the technique to derive a stronger (classical complexity theoretic) result, showing that the problem of finding the minimum number of tile types that uniquely assemble a given finite shape is ΣP2-complete. In contrast, the problem of finding the minimum number of deterministic tile types that uniquely assemble a shape is NP-complete [5].