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80
Algorithmic SelfAssembly of DNA
, 1998
"... How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, ..."
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Cited by 104 (6 self)
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How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNAbased computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNAbased computer  the selfassembly of DNA by hybridization and formation of the double helix  and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsawshaped tiles can be designed to simulate the operation of any Turing Machine. I propose...
Simulations of Computing by SelfAssembly
, 1998
"... Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleo ..."
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Cited by 69 (15 self)
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Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths. 1 Introduction Early work in DNA computing (Adleman 1994; Lipton 1995; Boneh et al. 1996; Ouyang et al. 1997) showed how computations can be accomplished by first creating a combinatorial library of DNA and then, through successiv...
Simulating Boolean Circuits on a DNA Computer
, 1997
"... We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are jrequen,tly encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix mult ..."
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Cited by 55 (9 self)
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We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are jrequen,tly encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semiunbounded janin Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC¹, the slowdown can be reduced to a constant. In this algorathm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequencespecific annealing, ligation, separation by size, amplification, sequencespecific cleavage, and detection by size. Additional steps of amplification are not necessary for NC¹ circuits. Preliminary biochemical experiments on a small test circuit have produced encouraging results. Further confirmatory experiments are in progress.
Towards parallel evaluation and learning of boolean µformulas with molecules
 Proc. of DNA 3 (H.Rubin, D.Wood, Eds.) DIMACS 48
, 1997
"... A {formula is a Boolean formula in which each variable occurs at most once. The paper treats its molecular representation including its queries using techniques in molecular biology. The novelty is that this method can evaluate a Boolean formula in a single tube within a short time. The preliminary ..."
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Cited by 34 (3 self)
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A {formula is a Boolean formula in which each variable occurs at most once. The paper treats its molecular representation including its queries using techniques in molecular biology. The novelty is that this method can evaluate a Boolean formula in a single tube within a short time. The preliminary experimental result suggests the possibility of parallel evaluation and learning of general {formulas. This method is essentially a simulation of state transitions and can be used to simulate a decision tree or a state machine. 1
Errorresistant Implementation of DNA Computations
 In Second Annual Meeting on DNA Based Computers
"... This paper introduces a new model of computation that employs the tools of molecular biology whose in vitro implementation is far more errorresistant than extant proposals. We describe an abstraction of the model which lends itself to natural algorithmic description, particularly for problems in ..."
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Cited by 30 (5 self)
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This paper introduces a new model of computation that employs the tools of molecular biology whose in vitro implementation is far more errorresistant than extant proposals. We describe an abstraction of the model which lends itself to natural algorithmic description, particularly for problems in the complexity class NP . In addition we describe a number of lineartime algorithms within our model, particularly for NP complete problems. We describe an in vitro realisation of the model and conclude with a discussion of future work. 1 Introduction The idea that living cells and molecular complexes can be viewed as potential machinic components dates back to the late 1950s, when Richard Feynman delivered his famous paper [4] describing "submicroscopic" computers. More recently, several papers [1, 10, 16] (also see [7, 13]) have advocated the realisation of massively parallel computation using the techniques and chemistry of molecular biology. Adleman describes how a computational...
A Survey of ContinuousTime Computation Theory
 Advances in Algorithms, Languages, and Complexity
, 1997
"... Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists o ..."
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Cited by 29 (6 self)
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Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists on the general theory of continuoustime models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. 1 Introduction After a long period of oblivion, interest in analog computation is again on the rise. The immediate cause for this new wave of activity is surely the success of the neural networks "revolution", which has provided hardware designers with several new numerically based, computationally interesting models that are structurally sufficiently simple to be implemented directly in silicon. (For designs and actual implementations of neural models in VLSI, see e.g. [30, 45]). However, the more fundamental...
Arithmetic and Logic Operations with DNA
, 1997
"... A lot of current research in DNA computing has been directed towards solving difficult combinatorial search problems. However, for DNA computing to be applicable on a wider range of problems, support for basic computational operations such as logic operations like AND, OR and NOT and arithmetic oper ..."
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Cited by 23 (1 self)
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A lot of current research in DNA computing has been directed towards solving difficult combinatorial search problems. However, for DNA computing to be applicable on a wider range of problems, support for basic computational operations such as logic operations like AND, OR and NOT and arithmetic operations like addition and subtraction is necessary. Unlike search problems, which can be solved by generating all possible combinations and extracting the correct output, these operations mandate that only a unique output be generated by specific inputs. The question of suitability of DNA for such simple operations has so far largely been unaddressed. In this paper we describe a novel method for using DNA molecules to solve the basic arithmetic and logic operations. We also show that multiple rounds of operations can be performed in a single test tube, utilizing the output of an operation as an input for the next. Furthermore, the operations can be performed in a linear series or a seriesparallel fashion and operators can be mixed to form any operation sequence.
DNA algorithms for computing shortest paths
 Proceedings of Genetic Programming
, 1998
"... DNA computing has recently generated much interest as a result of pioneering work by Adleman and Lipton. Their DNA algorithms worked on graph representations but no indication was provided as to how information on the arcs between nodes on a graph could be handled. The aim of this paper is to ..."
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Cited by 21 (0 self)
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DNA computing has recently generated much interest as a result of pioneering work by Adleman and Lipton. Their DNA algorithms worked on graph representations but no indication was provided as to how information on the arcs between nodes on a graph could be handled. The aim of this paper is to extend the basic DNA algorithmic techniques of Adleman and Lipton by proposing a method for representing simple arc information  in this case, distances between cities in a simple map. It is also proposed that the real potential of DNA computing for solving computationally hard problems will only be realised when algorithmic steps which currently require manual intervention are replaced by executable DNA which operate on DNA strands in testtubes. 1 Computationally hard problems and DNA computing Both Adleman's (1994) and Lipton's (1995) algorithms deal with graphs where there are no labels on the arcs, nor is there any indication provided as to how such labels can be handl...
DNA Computing Based on Splicing: The Existence of Universal Computers
 THEORY OF COMPUTING SYSTEMS
, 1995
"... Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is ..."
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Cited by 19 (3 self)
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Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is added. We also show that there exist universal splicing systems with the properties above, i. e. there exists a universal splicing system with fixed components which can simulate the behaviour of any given splicing system, when an encoding of the particular splicing system is added to its set of axioms. In this way the possibility of designing programmable DNA computers based on the splicing operation is proved.