) Weiping Cai, Anne E. Condon, Robert M. Corn, Elton Glaser, Zhengdong Fei, Tony Frutos, Zhen Guo, Max G. Lagally, Qinghua Liu, Lloyd M. Smith, Andrew Thiel University of Wisconsin Madison, WI 57306 USA Abstract A new model of DNA computation that is based on surface chemistry is studied. Such computations involve the manipulation of DNA strands that are immobilized on a surface, rather than in solution as in the work of Adleman. Surface-based chemistry has been a critical technology in many recent advances in biochemistry and offers several advantages over solution-based chemistry, including simplified handling of samples and elimination of loss of strands, which reduce error in the computation. The main contribution of this paper is in showing that in principle, surface-based DNA chemistry can efficiently support general circuit computation on many inputs in parallel. To do this, an abstract model of computation that allows parallel manipulation of binary inputs is described. It is...

A goal of research on DNA computing is to solve problems that are beyond the capabilities of the fastest silicon-based supercomputers. Adleman and Lipton present exhaustive search algorithms for 3Sat and 3-Coloring, which can only be run on small instances and hence are not practical. In this paper, we show how improved algorithms can be developed for the 3-Coloring and Independent Set problems. Our algorithms use only the DNA operations proposed by Adleman and Lipton, but combine them in more powerful ways, and use polynomial preprocessing on a standard computer to tailor them to the specific instance to be solved. The main contribution of this paper is a more general model of DNA algorithms than that proposed by Lipton. We show that DNA computation for NP-complete problems can do more than just exhaustive search. Further research in this direction will help determine whether or not DNA computing is viable for NP-hard problems. A second contribution is the first analysis of errors that arise in generating the solution space for DNA computation.