Is Cook's Theorem Correct for DNA-Based Computing?

Cook’s Theorem [4, 5] is that if one algorithm for an NP-complete problem will be developed, then other problems will be solved by means of reduction to that problem. Cook’s Theorem has been demonstrated to be right in a general digital electronic computer. In this paper, we propose a DNA algorithm for solving the vertex-cover problem. It is demonstrated that if the size of a reduced NP-complete problem is equal to or less than that of the vertex-cover problem, then the proposed algorithm can be directly used for solving the reduced NP-complete problem and Cook’s Theorem is correct on DNA-based computing. Otherwise, Cook’s Theorem is incorrect on DNA-based computing and a new DNA algorithm should be developed from the characteristic of NP-complete problems.

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