New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
Communications of the ACM
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second 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
A Space-Efficient Randomized DNA Algorithm for k-SAT
DNA '00 Revised Papers from the 6th International Workshop on DNA-Based Computers: DNA Computing
Solving 3-Satisfiability in Less Then 1, 579n Steps
CSL '92 Selected Papers from the Workshop on Computer Science Logic
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
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
Arithmetic computation in the tile assembly model: Addition and multiplication
Theoretical Computer Science
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
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
Error suppression mechanisms for DNA tile self-assembly and their simulation
Natural Computing: an international journal
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
DNA13'07 Proceedings of the 13th international conference on DNA computing
Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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Self-assembly is a powerful process found in nature that guides simple objects assembling, on their own, into complex structures. Self-assembly is of interest to computer scientists because self-assembling systems can compute functions, assemble shapes, and guide distributed robotics systems. The tile assembly model is a formal mathematical model of self-assembly that allows the study of time and space complexities of self-assembling systems that lie at the heart of several molecular computer implementations and distributed computational software systems. These implementations and systems require efficient tile systems with small tilesets and fast execution times. The state of the art, however, requires vastly complex tile systems with large tilesets to implement fast algorithms. In this paper, I present $${\mathbb{S}}_{FS},$$ a tile system that decides 3-SAT by creating $$O^{\star}(1.8393^n)$$ nondeterministic assemblies in parallel, improving on the previous best known solution that requires $$\Uptheta(2^n)$$ such assemblies. This solution directly improves the feasibility of building molecular 3-SAT solvers and efficiency of distributed software. I formally prove the correctness of the system, the number of required parallel assemblies, that the size of the system's tileset is $$147 = \Uptheta(1),$$ and that the assembly time is nondeterministic linear in the size of the input.