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144
Steps toward artificial intelligence
 Computers and Thought
, 1961
"... Harvard University. The work toward attaining "artificial intelligence’ ’ is the center of considerable computer research, design, and application. The field is in its starting transient, characterized by many varied and independent efforts. Marvin Minsky has been requested to draw this work to ..."
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Cited by 185 (0 self)
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Harvard University. The work toward attaining "artificial intelligence’ ’ is the center of considerable computer research, design, and application. The field is in its starting transient, characterized by many varied and independent efforts. Marvin Minsky has been requested to draw this work together into a coherent summary, supplement it with appropriate explanatory or theoretical noncomputer information, and introduce his assessment of the state of the art. This paper emphasizes the class of activities in which a generalpurpose computer, complete with a library of basic programs, is further programmed to perform operations leading to ever higherlevel information processing functions such as learning and problem solving. This informative article will be of real interest to both the general Proceedings reader and the computer specialist. The Guest Editor.
Wang Tiles for Image and Texture Generation
, 2003
"... We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, ..."
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Cited by 128 (4 self)
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We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, large expanses of nonperiodic texture (or patterns or geometry) can be created as needed very efficiently at runtime. Wang Tiles
Algorithmic selfassembly of DNA Sierpinski triangles
 PLoS Biology
"... Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular selfassembly. Here we report the molecular realization, using twodimensional selfassembly of DNA tiles, of a cellular automat ..."
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Cited by 104 (10 self)
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Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular selfassembly. Here we report the molecular realization, using twodimensional selfassembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on doublecrossover motifs. Serving as input for the computation, long singlestranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100–200 correct tiles. Error rates during assembly appear to range from 1 % to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA selfassembly can be treated as a Turinguniversal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks.
Running Time and Program Size for Selfassembled Squares
, 2001
"... Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by selfassembly. 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 ..."
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Cited by 70 (8 self)
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Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by selfassembly. 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 RothemundWinfree construction of n \Theta n squares requires time \Theta(n log n) and program size \Theta(log n). We present a new construction for assembling n \Theta n squares which uses optimal time \Theta(n) and program size \Theta( log n log log n ). This program size is also optimal since it matches the bound dictated by Kolmogorov complexity. Our improved time is achieved by demonstrating a set of tiles for parallel selfassembly of binary counters. Our improved program size is achieved by demonstrating that selfassembling systems can compute changes in the base representation of numbers. Selfassembly is emerging as a useful paradigm for computation. In addition the development of a computational theory of selfassembly promises to provide a new conduit by which results and methods of theoretical computer science might be applied to problems of interest in biology and the physical sciences. 1
COMPLEXITY OF SELFASSEMBLED SHAPES
, 2007
"... The connection between selfassembly and computation suggests that a shape can be considered the output of a selfassembly “program,” a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest selfassembly program that builds a shape and the shape’s descrip ..."
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Cited by 60 (4 self)
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The connection between selfassembly and computation suggests that a shape can be considered the output of a selfassembly “program,” a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest selfassembly program that builds a shape and the shape’s descriptional (Kolmogorov) complexity should be related. We show that when using a notion of a shape that is independent of scale, this is indeed so: in the tile assembly model, the minimal number of distinct tile types necessary to selfassemble a shape, at some scale, can be bounded both above and below in terms of the shape’s Kolmogorov complexity. As part of the proof, we develop a universal constructor for this model of selfassembly that can execute an arbitrary Turing machine program specifying how to grow a shape. Our result implies, somewhat counterintuitively, that selfassembly of a scaledup version of a shape often requires fewer tile types. Furthermore, the independence of scale in selfassembly theory appears to play the same crucial role as the independence of running time in the theory of computability. This leads to an elegant formulation of languages of shapes generated by selfassembly. Considering functions from bit strings to shapes, we show that the runningtime complexity, with respect to Turing machines, is polynomially equivalent to the scale complexity of the same function implemented via selfassembly by a finite set of tile types. Our results also hold for shapes defined by Wang tiling—where there is no sense of a selfassembly process—except that here time complexity must be measured with respect to nondeterministic Turing machines.
Local parallel biomolecular computing
 DNA Based Computers III, volume 48 of DIMACS
, 1999
"... Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP r ..."
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Cited by 51 (15 self)
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Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP requires that the computation execute sequentially within any given molecule (though done in parallel for multiple molecules). In contrast, local parallelism (LP) allows operations to be executed in parallel on each given molecule. Winfree, et al [W96, WYS96]) proposed an innovative method for LPBMC, that of computation by unmediated selfassembly of � arrays of DNA molecules, applying known domino tiling techniques (see Buchi [B62], Berger [B66], Robinson [R71], and Lewis and Papadimitriou [LP81]) in combination with the DNA selfassembly techniques of Seeman et al [SZC94]. The likelihood for successful unmediated selfassembly of computations has not been determined (we discuss a simple model of assembly where there may be blockages in selfassembly, but more sophisticated models may have a higher likelihood of success). We develop improved techniques to more fully exploit the potential power of LPBMC. To increase
Proofreading tile sets: Error correction for algorithmic selfassembly
 In DNA Based Computers 9, volume 2943 of LNCS
, 2004
"... Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low ..."
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Cited by 47 (10 self)
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Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate – but at the cost of reduced speed (r) for the selfassembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε 2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r ≈ βε and better. This suggests that existing DNAbased molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed. 1
The Structure of the Models of Decidable Monadic Theories of Graphs
, 1991
"... In this article the structure of the models of decidable (weak) monadic theories of planar graphs is investigated. It is shown that if the (weak) monadic theory of a class K of planar graphs is decidable, then the treewidth in the sense of Robertson and Seymour (1984) of the elements of K is univer ..."
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Cited by 44 (2 self)
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In this article the structure of the models of decidable (weak) monadic theories of planar graphs is investigated. It is shown that if the (weak) monadic theory of a class K of planar graphs is decidable, then the treewidth in the sense of Robertson and Seymour (1984) of the elements of K is universally bounded and there is a class T of trees such that the (weak) monadic theory of K is interpretable in the (weak) monadic theory of T.
Selfassembled circuit patterns
 In DNA Computing 9
, 2004
"... Abstract. Selfassembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudocrystalline selfassembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. ..."
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Cited by 41 (13 self)
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Abstract. Selfassembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudocrystalline selfassembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. This theoretical work builds on the theory of twodimensional tilings [8], using rigid square tiles called Wang tiles [24] for the basic units of selfassembly, and leads to Turinguniversal models such as the Tile Assembly Model [28]. Using the Tile Assembly Model, we show how algorithmic selfassembly can be exploited for fabrication tasks such as constructing the patterns that define certain digital circuits, including demultiplexers, RAM arrays, pseudowavelet transforms, and Hadamard transforms. Since DNA selfassembly appears to be promising for implementing the arbitrary Wang tiles [30, 13] needed for programming in the Tile Assembly Model, algorithmic selfassembly methods such as those presented in this paper may eventually become a viable method of arranging molecular electronic components [18], such as carbon nanotubes [10, 1], into molecularscale circuits. 1
Complexities for Generalized Models of SelfAssembly
 In SODA
, 2004
"... Abstract. In this paper, we study the complexity of selfassembly under models that are natural generalizations of the tile selfassembly model. In particular, we extend Rothemund and Winfree’s log N study of the tile complexity of tile selfassembly [9]. They provided a lower bound of Ω ( log log N ..."
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Cited by 38 (4 self)
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Abstract. In this paper, we study the complexity of selfassembly under models that are natural generalizations of the tile selfassembly model. In particular, we extend Rothemund and Winfree’s log N study of the tile complexity of tile selfassembly [9]. They provided a lower bound of Ω ( log log N) 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 selfassembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size O ( √ log N) which assembles an N × N square in a model which allows flexible glue strength between nonequal glues. This result is matched for almost all N by a lower bound dictated by log N Kolmogorov complexity. For three other generalizations, we show that the Ω ( ) lower bound log log N applies to N × N squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length N and width k, we provide a tighter lower bound of Ω ( N 1 k k log N construction which achieves O ( log log N) for the standard model, yet we also give a) complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape; we show that this problem is NPhard for three of the generalized models.