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
A Discreet, Fault-Tolerant, and Scalable Software Architectural Style for Internet-Sized Networks
ICSE COMPANION '07 Companion to the proceedings of the 29th International Conference on Software Engineering
An Architectural Style for Solving Computationally Intensive Problems on Large Networks
ICSEW '07 Proceedings of the 29th International Conference on Software Engineering Workshops
Fault and adversary tolerance as an emergent property of distributed systems' software architectures
Proceedings of the 2007 workshop on Engineering fault tolerant systems
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
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
Solving NP-complete problems in the tile assembly model
Theoretical Computer Science
Solving satisfiability in the tile assembly model with a constant-size tileset
Journal of Algorithms
Path finding in the tile assembly model
Theoretical Computer Science
Crystal-growth-inspired algorithms for computational grids
BADS '09 Proceedings of the 2009 workshop on Bio-inspired algorithms for distributed systems
Application of DNA Computing by Self-assembly on 0-1 Knapsack Problem
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Constant-size tileset for solving an NP-complete problem in nondeterministic linear time
DNA13'07 Proceedings of the 13th international conference on DNA computing
Improving efficiency of 3-SAT-solving tile systems
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Efficient 3-SAT algorithms in the tile assembly model
Natural Computing: an international journal
| Hi-index | 5.23 |
Formalized study of self-assembly has led to the definition of the tile assembly model, Previously I presented ways to compute arithmetic functions, such as addition and multiplication, in the tile assembly model: a highly distributed parallel model of computation that may be implemented using molecules or a large computer network such as the Internet. Here, I present tile assembly model systems that factor numbers nondeterministically using @Q(1) distinct components. The computation takes advantage of nondeterminism, but theoretically, each of the nondeterministic paths is executed in parallel, yielding the solution in time linear in the size of the input, with high probability. I describe mechanisms for finding the successful solutions among the many parallel executions and explore bounds on the probability of such a nondeterministic system succeeding and prove that the probability can be made arbitrarily close to 1.