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The first example of DNA computing used "brute force", in which random DNA molecules were generated, and then the correct sequence was identified. The first problem solved by DNA computations involved finding the optimal path by which a travelling salesman could visit a fixed number of cities once each.

Regardless of the approach, many technological challenges remain before DNA computing can be widely used. Researchers must develop techniques to reduce the number of computational errors produced by unwanted chemical reactions with the DNA strands. And they need to eliminate, combine, or accelerate the steps in processing the DNA.

Recent work has shown how DNA can be employed to carry out a fundamental computer operation, addition of two numbers expressed in binary

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Utilising DNA, in computing, when attached to a surface seams like the most significant step forward from test-tube reactions. One particular example is to attach the DNA molecules to gold-coated square of glass. This 'solid surface' chemistry greatly simplifies the complex and repetitive steps previously used in rudimentary DNA computers

This approach is something akin to a conventional memory chip. As many as a trillion individual strands of DNA can be anchored to the glass, each strand containing information being stored in the DNA computer. However much more DNA could be contained within a three dimensional volume of a test-tube. 

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To use a solid surface the scientists must immobilize a complete combinatorial set of single strand DNA oligomers onto a surface. The surface will facilitate sample handling and simplify reactant-product separation. There will however be a loss of information density in this two-dimensional world and slower enzyme movement. This is why (link) Adleman's research remains in test tubes. 

“Putting DNA computing on a solid surface makes the technology simpler, more accessible and more amenable to being scaled up to make computers.”

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