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
Introduction to the Theory of Computation
Introduction to the Theory of Computation
On the Decidability of Self-Assembly of Infinite Ribbons
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
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
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Arithmetic computation in the tile assembly model: Addition and multiplication
Theoretical Computer Science
An Architectural Style for Solving Computationally Intensive Problems on Large Networks
ICSEW '07 Proceedings of the 29th International Conference on Software Engineering Workshops
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
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
DNA'04 Proceedings of the 10th 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
Crystal-growth-inspired algorithms for computational grids
BADS '09 Proceedings of the 2009 workshop on Bio-inspired algorithms for distributed systems
Improving efficiency of 3-SAT-solving tile systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Generalized gandy-păun-rozenberg machines for tile systems and cellular automata
CMC'11 Proceedings of the 12th international conference on Membrane Computing
Efficient 3-SAT algorithms in the tile assembly model
Natural Computing: an international journal
A Molecular Solution to the Three-Partition Problem
Journal of Information Technology Research
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Biological systems are far more complex and robust than systems we can engineer today. One way to increase the complexity and robustness of our engineered systems is to study how biological systems function. The tile assembly model is a highly distributed parallel model of nature's self-assembly. Previously, I defined deterministic and nondeterministic computation in the tile assembly model and showed how to add, multiply, factor, and solve SubsetSum. Here, I present a system that decides satisfiability, a well-known NP-complete problem. The computation is nondeterministic and each parallel assembly executes in time linear in the input. The system requires only a constant number of different tile types: 64, an improvement over previously best known system that uses @Q(n^2) tile types. I describe mechanisms for finding the successful solutions among the many parallel assemblies and explore bounds on the probability of such a nondeterministic system succeeding and prove that probability can be made arbitrarily close to 1.