DNA-Based Computation Times

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Presentation transcript:

DNA-Based Computation Times Y. Baryshnikov, E. Coffman, and P. Momcilovic Preliminary Proceedings of the 10th International Meeting on DNA Computing, pp. 173-182, 2004. Cho, Dong-Yeon

© 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

© 2004 SNU CSE Biointelligence Lab 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. © 2004 SNU CSE Biointelligence Lab

DNA Computation of Boolean Formulas An Example I: input N: NAND *: Null L, R: forwarding [Carbone and Seeman, 2002] © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab 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. © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab 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. © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab Growth Models (3/5) Computation of Arbitrary Shapes : 1 : 0 p + q = 1 © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab 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 © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab Growth Models (5/5) © 2004 SNU CSE Biointelligence Lab

© 2004 SNU CSE Biointelligence Lab 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 © 2004 SNU CSE Biointelligence Lab