DNA models and algorithms for NP-complete problems
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Using DNA to solve the bounded Post correspondence problem
Theoretical Computer Science - Special issue on universal machines and computations
A polymerase based algorithm for SAT
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
DNA'04 Proceedings of the 10th international conference on DNA computing
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Adleman reported how to solve a 7-vertex instance of the Hamiltonlan path problem by means of DNA manipulations. After that a major goal of subsequent research is how to use DNA manipulations to solve NP-hard problems, especially 3-SAT problems. Lipton proposed DNA experiments on test tubes to solve 3-SAT problems. Liu et al. reported how to solve a simple case of 3-SAT using DNA computing on surfaces. Lipton's model of DNA computing is simple and intuitive for 3-SAT problems. The separate (or extract) operation, which is a key manipulation of DNA computing, only extracts some of the required DNA strands and Lipton thinks that a typical percentage might be 90. But it is unknown what would happen due to imperfect extract operation. Let p be the rate, where 0 p s in a test tube, there are 10l (l=13 proposed by Adleman) copies of s and that extracting each of the required DNA strands is equally likely. Here, the present paper will report, no matter how large l is and no matter how close to 1 p is, there always exists a class of 3-SAT problems such that DNA computing error must occur. Therefore, DNA computing is not viable for 3-SAT.