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190
The program-size complexity of self-assembled squares
- In Proceedings of the thirty-second annual ACM symposium on Theory of computing
, 2000
"... ..."
Running Time and Program Size for Self-assembled Squares
, 2001
"... Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by self-assembly. Here, we consider the time complexity of such constructions using a natural generalization of the Tile Assembly Model defined in [6]. In the generalized model, the RothemundWinf ..."
Abstract
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Cited by 96 (8 self)
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Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by self-assembly. Here, we consider the time complexity of such constructions using a natural generalization of the Tile Assembly Model defined in [6]. In the generalized model, the Rothemund
Assemble time for self-assembling square tiles
, 2004
"... ... methods of assembling these components become ever more impractical. Self-assembly is a viable solution in which the individual components autonomously organize themselves without the external guidance of a supervising agent. In this paper we look at the assembly times for various one and two di ..."
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... methods of assembling these components become ever more impractical. Self-assembly is a viable solution in which the individual components autonomously organize themselves without the external guidance of a supervising agent. In this paper we look at the assembly times for various one and two
Parallelism and Time in Hierarchical Self-Assembly
, 2012
"... We study the role that parallelism plays in time complexity of variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the “hierarchical ” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the ..."
Abstract
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Cited by 17 (6 self)
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in the “seeded” aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang (Running Time and Program Size for Self-Assembled Squares, STOC 2001) showed how to assemble an n×n square in O(n) time in log n the seeded aTAM using O ( ) unique tile types, where log log n both
Self-assembled circuit patterns
- In DNA Computing 9
, 2004
"... Abstract. Self-assembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudo-crystalline self-assembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. ..."
Abstract
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Cited by 44 (14 self)
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]. This theoretical work builds on the theory of twodimensional tilings [8], using rigid square tiles called Wang tiles [24] for the basic units of self-assembly, and leads to Turing-universal models such as the Tile Assembly Model [28]. Using the Tile Assembly Model, we show how algorithmic self-assembly can
Triangular Self-Assembly
, 2010
"... We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic ornon-deterministic, has thesame power tothesquare tileassembly system incomp ..."
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We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic ornon-deterministic, has thesame power tothesquare tileassembly system
Complexities for Generalized Models of Self-Assembly
- IN SODA
, 2004
"... In this paper, we study the complexity of self-assembly under models that are natural generalizations of the tile self-assembly model. In particular, we extend Rothemund and Winfree’s log N study of the tile complexity of tile self-assembly [9]. They provided a lower bound of Ω ( log log N) on the ..."
Abstract
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Cited by 52 (6 self)
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) on the tile complexity of assembling an N × N square for almost all N. Adleman et al. [1] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size O
OPTIMAL TIME SELF-ASSEMBLY FOR SQUARES AND CUBES
"... ABSTRACT. We refine the current notion of time in self-assembly, and show constructions which are timeoptimal, not only up to a constant. For this, we refine the notion of time-complexity of an assembly, to separate the influence of the concentrations from the intrinsic speed of the assembly. We giv ..."
Abstract
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ABSTRACT. We refine the current notion of time in self-assembly, and show constructions which are timeoptimal, not only up to a constant. For this, we refine the notion of time-complexity of an assembly, to separate the influence of the concentrations from the intrinsic speed of the assembly. We
Results 1 - 10
of
190
