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
Arithmetic computation in the tile assembly model: Addition and multiplication
Theoretical Computer Science
An Architectural Style for Solving Computationally Intensive Problems on Large Networks
SEAMS '07 Proceedings of the 2007 International Workshop on Software Engineering for Adaptive and Self-Managing Systems
Fault and adversary tolerance as an emergent property of distributed systems' software architectures
Proceedings of the 2007 workshop on Engineering fault tolerant systems
Nondeterministic polynomial time factoring in the tile assembly model
Theoretical Computer Science
Solving NP-complete problems in the tile assembly model
Theoretical Computer Science
Self-correcting self-assembly: growth models and the hammersley process
DNA'05 Proceedings of the 11th international conference on DNA Computing
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
Programming and evolving physical self-assembling systems in three dimensions
Natural Computing: an international journal
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The tile assembly model, a formal model of crystal growth, is of special interest to computer scientists and mathematicians because it is universal [1]. Therefore, tile assembly model systems can compute all the functions that computers compute. In this paper, I formally define what it means for a system to nondeterministically decide a set, and present a system that solves an NP-complete problem called SubsetSum. Because of the nature of NP-complete problems, this system can be used to solve all NP problems in polynomial time, with high probability. While the proof that the tile assembly model is universal [2] implies the construction of such systems, those systems are in some sense "large" and "slow." The system presented here uses 49 = Θ(1) different tiles and computes in time linear in the input size. I also propose how such systems can be leveraged to program large distributed software systems.