DNA Computing and Molecular Programming: 18th International by Bahar Behsaz, Ján Maňuch, Ladislav Stacho (auth.), Darko

By Bahar Behsaz, Ján Maňuch, Ladislav Stacho (auth.), Darko Stefanovic, Andrew Turberfield (eds.)

This e-book constitutes the refereed court cases of the 18th foreign convention on DNA Computing and Molecular Programming, DNA 18, held in Aarhus, Denmark, in August 2012. The eleven complete papers provided have been rigorously chosen from 37 submissions. The papers are geared up in topical sections on advancing the engineering and technology of biology and chemistry from the viewpoint of laptop technology, physics, and mathematics.

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Additional info for DNA Computing and Molecular Programming: 18th International Conference, DNA 18, Aarhus, Denmark, August 14-17, 2012. Proceedings

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Xk ) = (#Y1 , . . , #Yl ). 1. f (#0 X1 , . . , #0 Xk )i = #0 YiC for all i ∈ {1, . . , l}: Then #↑∞ YiP = #↑∞ YiC for all i ∈ {1, . . 1). At this point there are some number of L0 ’s and L1 ’s remaining. 1) created a copy of L1 . 3) are possible, #L1 stays positive forever. 4) eventually removes all copies of L0 . 2. f (#0 X1 , . . , #0 Xk )i = #0 YiC for some i ∈ {1, . . , l}: Then #↑∞ YiP = #↑∞YiC for some i ∈ {1, . . 1) ensures that eventually either 1) #∞ YiC = 0 and #∞ YiP > 0, or 2) #∞ YiC > 0 and #∞ YiP = 0.

L. Chen, D. Doty, and D. Soloveichik molecules based on the weighted sum of the aji coefficients. Therefore when all Xij molecules are consumed, the number of Yj molecules is the proper value yj = bj + ki=1 aji (xi + ci ). It remains to analyze the expected completion time. Let n = x . Since the total number of molecules in solution at any time is O(n), the volume required is also O(n). We measure the time to consume all Xi molecules for all i. We start with n such molecules, so the time for all of them to convert is the maximum of n exponential random variables, each with constant expected value, which is O(log n).

0 YlC ), then #∞ L1 > 0 and #∞ L0 = 0, and otherwise, #∞ L1 = 0 and #∞ L0 > 0, showing that D stably decides the graph of f . 1. Intuitively, it uses a random search of the output space to look for the correct answer to the function and uses a predicate decider to check whether the correct solution has been found. 2. Every semilinear function is stably computable by a CRC. Proof. Let f : Nk → Nl be a semilinear function, and let F = (x, y) ∈ Nk × Nl f (x) = y denote the graph of f . We then consider the set F = (x, yP , yC ) ∈ Nk × Nl × Nl f (x) = yP − yC .

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