I co-wrote a thesis which touches this type of problems. The idea is that DNA is a very concentrated and massively parallel computing medium. However after all it's only kicking the can along the road. Citing myself:
«If we had a computer based on chemistry working a million times faster, then we could add twenty more variables to the SAT problem (the dual logarithm of a million is roughly 20). This is better, but not much better. If we want to add 100 more variables, we would run into problems. Suppose we need 2^100 water molecules with a molecular weight of around 18, then they would weigh 18·2^100/NA ≈ 38·10^6 grams or around 38 tons (NA being Avogadro’s number). With a few more variables we would need more water than there is available on the earth. This is the limitation of the memory for time tradeoff.»