1. DNA-Based Computation Times
Y. Baryshnikov, E. Coffman, and P. Momcilovic
Preliminary Proceedings of the 10th International Meeting on DNA Computing, pp , 2004.
Cho, Dong-Yeon

2. © 2004 SNU CSE Biointelligence Lab
Abstract
Speed of Computation and Power Consumption
While DNA-based computational devices are known to be extremely energy efficient, little is known concerning the fundamental question of computation times.
In particular, given a function, we study the time required to determine its value for a given input.
© 2004 SNU CSE Biointelligence Lab

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Introduction
Self-Assembly Process
Successive bonding of tiles performs a computation.
The evaluation of a Boolean formula on given inputs
The tiles are DNA-based molecular structures moving randomly, in solution, and capable of functioning independently and in parallel in the self-assembly process.
The template is needed to properly structure the self-assembly.
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4. DNA Computation of Boolean Formulas
An Example
I: input
N: NAND
*: Null
L, R: forwarding
[Carbone and Seeman, 2002]
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Growth Models (1/5)
Rectangle Computation
Attachment Time: Ti,j
Independent exponential random variables with unit means
Completion time
Initial condition: Ci,1= C1,j = 0 for 1  i  M and 1  j  N
The maximum is taken over all paths  from (1,1) to (M,N) consisting of segments going north or east only.
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Growth Models (2/5)
Totally asymmetric simple exclusion process (TASEP)
A square template of size NN: CN,N  4N
Ex) let the required computation time be 1 second and N = 103. Then, the mean of attachment time should be 1/(4· 103) = 0.25 milliseconds.
Observations
The prefabrication of the input might be the actual bottleneck of the computation.
Higher speed requires smaller attachment times, i.e., higher molecular mobility, which can result in higher error rates.
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Growth Models (3/5)
Computation of Arbitrary Shapes
: 1
: 0
p + q = 1
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Growth Models (4/5)
Let v(x, y) be the time needed for the boundary to reach point (x, y).
Given vx and vy are partial derivatives of v
Partial differential equation (Hamilton-Jacobi equation)
The Legendre dual to H
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Growth Models (5/5)
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Concluding Remarks
Result
The hydrodynamic limits of the computation times for 2D DNA-based logical devices
Nonhomogeneous and/or non-Markovian
0.5
0.9
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