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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 103 (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...
On the Computational Power of DNA Annealing and Ligation
 DNA Based Computers, volume 27 of DIMACS
, 1995
"... In [Winfree] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [Boneh] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, " ..."
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Cited by 74 (18 self)
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In [Winfree] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [Boneh] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify necessary at all?" This paper proposes to informally explore the power of annealing and ligation for DNA computation. We conclude, in fact, that annealing and ligation alone are theoretically capable of universal computation. 1 Introduction When Len Adleman introduced the paradigm of using DNA to solve combinatorial problems [Adleman], his computational scheme involved two distinct phases. To solve the directed Hamiltonian path problem, he first mixed together in a test tube a carefully designed set of DNA oligonucleotide "building blocks", which anneal to each other and are ligated to create long strands of DNA representing paths t...
Breaking DES Using a Molecular Computer
, 1995
"... Recently Adleman [1] has shown that a small traveling salesman problem can be solved by molecular operations. In this paper we show how the same principles can be applied to breaking the Data Encryption Standard (DES). Our method is based on an encoding technique presented in Lipton [8]. We describe ..."
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Cited by 56 (4 self)
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Recently Adleman [1] has shown that a small traveling salesman problem can be solved by molecular operations. In this paper we show how the same principles can be applied to breaking the Data Encryption Standard (DES). Our method is based on an encoding technique presented in Lipton [8]. We describe in detail a library of operations which are useful when working with a molecular computer. We estimate that given one arbitrary (plaintext, ciphertext) pair, one can recover the DES key in about 4 months of work. Furthermore, if one is given ciphertext, but the plain text is only known to be one of several candidates then it is still possible to recover the key in about 4 months of work. Finally, under chosen ciphertext attack it is possible to recover the DES key in one day using some preprocessing. 1 Introduction Due to advances in molecular biology it is nowadays possible to create a soup of roughly 10 18 DNA strands that fits in a small glass of water. Adleman [1] has shown that e...
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
Making DNA computers error resistant
, 1995
"... We describe methods for making volume decreasing algorithms more resistant to certain types of errors. Such error recovery techniques are crucial if DNA computers ever become practical. Our first approach relies on applying PCR at various stages of the computation. We analyze its performance and sho ..."
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Cited by 37 (4 self)
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We describe methods for making volume decreasing algorithms more resistant to certain types of errors. Such error recovery techniques are crucial if DNA computers ever become practical. Our first approach relies on applying PCR at various stages of the computation. We analyze its performance and show that it increases the survivalprobability of various strands to acceptable proportions. Our second approach relies on changing the method by which information is encoded on DNA strands. This encoding is likely to reduce false negative errors during the bead separation procedure. 1 Introduction In the short history of DNA (deoxyribonucleic acid) based computing there have already been a number of exciting results. It all started with Adleman's [A] beautiful insight that showed that biological experiments could solve the Directed Hamiltonian Path problem (DHP). Then, Lipton [L] showed how to use DNA to solve more general problems, namely to find satisfying assignments for arbitrary (direct...
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...
DNA Simulation of Boolean Circuits
 Proceedings of 3rd Annual Genetic Programming Conference
, 1997
"... In this paper we describe a simulation of Boolean circuits using standard biomolecular techniques. Previously proposed simulations have been shown to run in time proportional to the size of the circuit. The simulation we present here runs in time proportional to the depth of the circuit. We describ ..."
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Cited by 25 (1 self)
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In this paper we describe a simulation of Boolean circuits using standard biomolecular techniques. Previously proposed simulations have been shown to run in time proportional to the size of the circuit. The simulation we present here runs in time proportional to the depth of the circuit. We describe the abstract model and its laboratory implementation, before concluding with a brief analysis.