1. Department of Chemistry,
2. Department of Computer Science, University of Wisconsin, Madison, Wisconsin 53706, USA
3. Present addresses: Gen-Probe, Inc. , San Diego, California 92121, USA (Q.L.); Corning Inc., Corning, New York 14831, USA (A.G.F.); Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (A.E.C.).

Correspondence to: Lloyd M. Smith¹ Correspondence and requests for materials should be addressed to L.M.S. (e-mail: Email: smith@chem.wisc.edu)

DNA computing was proposed¹ as a means of solving a class of intractable computational problems in which the computing time can grow exponentially with problem size (the 'NP-complete' or non-deterministic polynomial time complete problems). The principle of the technique has been demonstrated experimentally for a simple example of the hamiltonian path problem² (in this case, finding an airline flight path between several cities, such that each city is visited only once³). DNA computational approaches to the solution of other problems have also been investigated^{4, 5, 6, 7, 8, 9}. One technique^{10, 11, 12, 13} involves the immobilization and manipulation of combinatorial mixtures of DNA on a support. A set of DNA molecules encoding all candidate solutions to the computational problem of interest is synthesized and attached to the surface. Successive cycles of hybridization operations and exonuclease digestion are used to identify and eliminate those members of the set that are not solutions. Upon completion of all the multi-step cycles, the solution to the computational problem is identified using a polymerase chain reaction to amplify the remaining molecules, which are then hybridized to an addressed array. The advantages of this approach are its scalability and potential to be automated (the use of solid-phase formats simplifies the complex repetitive chemical processes, as has been demonstrated in DNA and protein synthesis¹⁴). Here we report the use of this method to solve a NP-complete problem. We consider a small example of the satisfiability problem (SAT)², in which the values of a set of boolean variables satisfying certain logical constraints are determined.