## Error-resistant Implementation of DNA Computations (0)

Venue: | In Second Annual Meeting on DNA Based Computers |

Citations: | 30 - 5 self |

### BibTeX

@INPROCEEDINGS{Amos_error-resistantimplementation,

author = {Martyn Amos and Alan Gibbons and David Hodgson},

title = {Error-resistant Implementation of DNA Computations},

booktitle = {In Second Annual Meeting on DNA Based Computers},

year = {},

pages = {87--101}

}

### OpenURL

### Abstract

This paper introduces a new model of computation that employs the tools of molecular biology whose in vitro implementation is far more error-resistant 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 linear-time 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 "sub-microscopic" 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...

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Citation Context ...ly effective for algorithmic description. Moreover, it is sufficiently strong to solve any of the problems in the class NC which includes, of course, the notoriously intractable NP -complete problems =-=[10]-=-. As we shall see, these problems naturally have polynomial-time (often linear-time) parallel solutions within the model. This usually comes with the expense of exponentially large data sets. Within t... |

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Citation Context ... can be viewed as potential machinic components dates back to the late 1950s, when Richard Feynman delivered his famous paper [4] describing "sub-microscopic" computers. More recently, sever=-=al 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 computationally intractable proble... |

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Citation Context ...t P n can be a useful subprocedure for other computations. 2.3 Algorithms for a selection of NP-complete problems. We now describe a number of algorithms for graph-theoretic NP-complete problems (see =-=[6]-=-, for example). Problems in the complexity class NP seem to have a natural expression and ease of solution within the model. We describe linear-time solutions although, of course, there is frequently ... |

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Citation Context ...mplete problem. Our examples also demonstrate that individual NP-complete problems seem to have a natural and direct encoding for the model. It might be that the Parallel Random Access Machine (P-RAM =-=[5]-=-) or the Turing Machine can be directly simulated within the model which would establish that any algorithm can be realised by it. We have yet to pursue this line of research. 3 Implementation of the ... |

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Citation Context ... can be viewed as potential machinic components dates back to the late 1950s, when Richard Feynman delivered his famous paper [4] describing "sub-microscopic" computers. More recently, sever=-=al 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 computationally intractable proble... |

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Citation Context ...ng a CREW P-RAM in vitro. However, Reif uses the error-prone hybridization separation method described earlier, which we believe may be avoided by our methodology. Another development is the proposed =-=[15]-=- DNA and restriction enzyme implementation of Turing Machines. 11 The Turing Machine is, however, sequential in nature, and so the implementation of this does not exploit the inherent parallelism of D... |

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Citation Context ...ear-time 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 In the past =-=[9]-=- and more recently, several papers [1, 15, 21] (also see [12, 18]) have advocated the realisation of massively parallel computation using the techniques and chemistry of molecular biology. Adleman des... |

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Citation Context ...id computations than conventional computers on a range of feasible problem sizes. One possible way around the weight problem is to look for implementation of existing computing paradigms in DNA. Reif =-=[14]-=- points to one possible way forward, describing a method for simulating a CREW P-RAM in vitro. However, Reif uses the error-prone hybridization separation method described earlier, which we believe ma... |

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Citation Context ...s at least one barrier to scalable DNA computation. This concerns the sheer weight of DNA required to solve any problems of large size in the model described in this paper. As Hartmanis points out in =-=[8], if Adlem-=-an's experiment were scaled up to 200 vertices the weight of DNA required would exceed that of the Earth. DNA computations, like all others, cannot escape the "exponential curse". The approa... |

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Citation Context ...entation of Turing Machines, which establishes formally that any algorithm can be realised through DNA, although Turing machine emulation is not likely to be of practical significance. Baum and Boneh =-=[3] describe -=-an alternative form of DNA computation which is not, in their words, "brute force". Their implied criticism is valid if it is directed at the notion of using exponential-sized volumes of DNA... |

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Citation Context ... can be viewed as potential machinic components dates back to the late 1950s, when Richard Feynman delivered his famous paper [4] describing "sub-microscopic" computers. More recently, sever=-=al 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 computationally intractable proble... |

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Citation Context ...A ligase [2]. This allows us to create a unified strand from several bound together by their respective complements. Another useful method of manipulating DNA is the Polymerase Chain Reaction, or PCR =-=[11, 12]-=-. PCR is a process that quickly amplifies the amount of DNA in a given solution. Each cycle of the reaction doubles the quantity of each strand, giving an exponential growth in the number of strands. ... |

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Citation Context ...ation as sequences of bases in DNA molecules, Adleman shows how existing DNA-manipulation techniques may be used to quickly detect and amplify desirable solutions to a given problem. A recent attempt =-=[9]-=- to repeat Adleman's experiment has cast doubt upon the efficacy of extant models of DNA computation. The researchers performed Adleman's experiment twice; once on the original graph as a positive con... |

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Citation Context ...by Sau3AI (b) The result 3. In double-stranded DNA, if one of the single strands contains a discontinuity (i.e., one nucleotide is not bonded to its neighbour) then this may be repaired by DNA ligase =-=[2]-=-. This allows us to create a unified strand from several bound together by their respective complements. Another useful method of manipulating DNA is the Polymerase Chain Reaction, or PCR [11, 12]. PC... |

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Citation Context ...eve the conditions whereby only correct hybridization occurs. Furthermore, as the length of the DNA strands being used increases, so does the probability of incorrect hybridization. Although attempts =-=[13]-=- have been made to simulate highly reliable extraction using a sequence of imperfect operations, it is clear that for any non-trivial problem, reliance on the extraction operation must be minimised, o... |

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Citation Context ...ntial machinic components dates back to the late 1950s, when Richard Feynman delivered his famous paper [4] describing "sub-microscopic" 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 computationally intractable problem, known as the di... |

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