Theoretical and Experimental DNA Computation (Natural ...

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Contents of M at start of simulation Simulation of changes made by A 1 Simulation of changes made by A 2 Simulation of changes made by A 3 Memory contents after A k−1 Simulation of changes made by A k Simulation of changes made by A R(n)−1 Simulation of changes made by A R(n) Output: final contents of M 4.11 Assessment 101 0 1 2 3 k R(n)−1 R(n) T(n) Fig. 4.10. Combinational circuit block simulation of control program
102 4 Complexity Issues best attainable (where S is the total space used by the P-RAM algorithm). One consequence of this is that the class, NC, of efficient parallel algorithms can be realized in DNA with only a small loss of speed and increase in size. We note some further points of interest about our simulation process. First, the translation from CREW P-RAM to DNA algorithm is an effective and practical one. It thus follows that, in at least one computational paradigm, the CREW P-RAM is an architecture that can be realized. This is despite the fact, noted by many researchers, that the technological overheads implied by a global common memory regime, to say nothing of the Concurrent Read facility, which means that within traditional silicon approaches the CREW P-RAM is not a constructible, scalable machine. In other words, our DNA realization gives a feasible, concrete implementation of what has been regarded as a purely abstract device. The second point concerns the nature of the translation process itself. Although no published CREW P-RAM algorithms are actually specified at the “machine code” level we regard as the basic processor instruction set, it is quite clear that, starting from a (sequential) program specified in an ersatz-ALGOL formalism, such algorithms could be compiled into a program over the basic instruction set specified in Table 4.4. It is also clear, however, that the process of translating the “assembly level” program to a combinational circuit specification is a mechanical one, and, furthermore, the creation of DNA strands from a given NAND circuit can also be performed automatically. If we combine these chains of ideas, then we see that a high − level CREW P-RAM to DNA compiler process is readily available. We now give a worked example of this compilation process. 4.12 A Worked Example: The List Ranking Problem We give, in this section, a worked example of the ideas presented above on a typical CREW P-RAM algorithm. The example we choose is the list ranking algorithm from [64]: given a list, L, ofn =2 m elements, the problem is to associate with each element k avaluerank(k) corresponding to its distance from the end of the list. For each list element k alocationnext(k) givesthe location of the next element in the list. For the last element, next(k) =k. We describe the algorithm as described in [64]: for all k ∈ L in parallel do begin P (k) :=next(k); if P (k) �= k then distance(k) :=1; else distance(k) :=0; end repeat log n times
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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
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Vector Strand to be inserted (targe
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1.5 Summary 1.6 Bibliographical Not
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24 2 Theoretical Computer Science:
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46 3 Models of Molecular Computatio
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48 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[])
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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
Page 126 and 127: 5.3 Initial Set Construction Within
Page 128 and 129: Vertex 1 Vertex 2 Vertex 3 ¡ ¡ ¡
Page 130 and 131: 5.5 Evaluation of Adleman’s Imple
Page 132 and 133: 5.6 Implementation of the Parallel
Page 134 and 135: 5.8 Experimental Investigations 119
Page 138 and 139: Create initial strand library Confi
Page 144 and 145: Experiment 25. New full-length chai
Page 150 and 151: 5.9 Other Laboratory Implementation
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Page 163 and 164: 148 6 Cellular Computing of truly i
Page 165 and 166: 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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