Theoretical and Experimental DNA Computation (Natural ...

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1 2 3 a f 1 2 3 a b 2 f 3.6 Summary 69 1 2 3 a 2 b a 3 b 4 f 8 f Initial configuration First iteration, n=1 Second iteration, n=2 Third iteration, n=3 1 1 1 1 2 2 2 2 3 4 b 4 d 4 d 4 e 4 d 8 e 16 f 8 f 4 f 2 f Fourth iteration, n=4, dissolve membrane 3 1 2 4 12 d e f 1 2 3 Replace b with d in Produce copies of e parallel, halve copies of f 1 4 16 d e Increase e, halve f f dissolves membrane 2 Send out copies of e, 1 d 4 Increase e, halve f e 16 Fig. 3.10. Execution of P system for n =4 In terms of their application, P systems have been used to solve instances of NP-complete problems, notably the Satisfiability and Hamiltonian Path Problems [165]. It is clear that the emerging field of P systems will provide a rich vein of both theoretical results and applications. As Gheorge Păun notes in [117], perhaps the most fundamental open question in the field concerns the physical realization of P systems. Perhaps research in the field of cellular computing (discussed in a later chapter) may provide further insights into this. 3.6 Summary In this chapter we categorized models of molecular computation into one of four types (filtering, splicing, constructive, and membrane). Abstract models of each type were described, as well as a selection of algorithms within them.
70 3 Models of Molecular Computation We payed particular attention to the filtering algorithms, especially those of Adleman, Lipton, and Amos et al. 3.7 Bibliographical Notes The Proceedings of the Second Annual Workshop on DNA Based Computers [94] are significant in that they contain descriptions of both the sticker model and the parallel filtering model, as well as an early paper of Winfree’s on selfassembly. Splicing systems are described in detail in [120], a comprehensive review of membrane computing is given in [119], and an assortment of essays dealing mainly with theoretical aspects of DNA computing is collected in [84]. Finally, [13] reviews topics in the theory of DNA computing.
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Natural Computing Series Series Edi
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Martyn Amos Department of Computer
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Preface DNA computation has emerged
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Preface IX acknowledged. Finally, I
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XII Contents 4 Complexity Issues ..
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Introduction “Where a calculator
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Introduction 3 Even though their un
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1 DNA: The Molecule of Life “All
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1.3 DNA as the Carrier of Genetic I
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1.3 DNA as the Carrier of Genetic I
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Synthesis 1.4 Operations on DNA 11
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Gel electrophoresis 1.4 Operations
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5’ 3’ A T A G A G T T 3’ TCA
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1.4 Operations on DNA 17 Others may
Page 34 and 35: Vector Strand to be inserted (targe
Page 36: 1.5 Summary 1.6 Bibliographical Not
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Page 61 and 62: 46 3 Models of Molecular Computatio
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Page 87 and 88: 72 4 Complexity Issues is that, alt
Page 89 and 90: 74 4 Complexity Issues The weak par
Page 91 and 92: 76 4 Complexity Issues 4.3 A Strong
Page 93 and 94: 78 4 Complexity Issues Ω = {∧,
Page 95 and 96: 80 4 Complexity Issues 0 1 0 1 x1 x
Page 97 and 98: 82 4 Complexity Issues connecting a
Page 99 and 100: 84 4 Complexity Issues Level simula
Page 101 and 102: 86 4 Complexity Issues At level D(S
Page 103 and 104: 88 4 Complexity Issues xANDy)) and
Page 105 and 106: 90 4 Complexity Issues Input matrix
Page 107 and 108: 92 4 Complexity Issues memory acces
Page 109 and 110: 94 4 Complexity Issues denoted by P
Page 111 and 112: 96 4 Complexity Issues The final st
Page 113 and 114: 98 4 Complexity Issues 1)), ADDR[])
Page 115 and 116: 100 4 Complexity Issues Size(STI)=O
Page 117 and 118: 102 4 Complexity Issues best attain
Page 119 and 120: 104 4 Complexity Issues 10. LDC 0 1
Page 121 and 122: 106 4 Complexity Issues ACC[] := bi
Page 124 and 125: 5 Physical Implementations “No am
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Page 128 and 129: Vertex 1 Vertex 2 Vertex 3 ¡ ¡ ¡
Page 130 and 131: 5.5 Evaluation of Adleman’s Imple
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5.8 Experimental Investigations 119
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Create initial strand library Confi
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Experiment 25. New full-length chai
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5.9 Other Laboratory Implementation
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5.11 Bibliographical Notes 145 whic
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148 6 Cellular Computing of truly i
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150 6 Cellular Computing 6.2 Succes
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152 6 Cellular Computing are “glu
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154 6 Cellular Computing x y z x (a
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156 6 Cellular Computing 6.7 Biblio
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158 References 14. Martyn Amos, Ste
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160 References 53. Dónall A. Mac D
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162 References 92. D. Knuth. The Ar
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164 References 135. Kensaku Sakamot
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Index ALGOL, 102 AND, 23-24, 42, 87
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iological, 74, 114, 150 Feynman, R.
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Petrinet,63 phage, 18-20 phosphate,
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Natural Computing Series W.M. Spear
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