DNA computing is a form of parallel computing in that it takes advantage of the many different molecules of DNA to try many different possibilities at once. For certain specialized problems, DNA computers are faster and smaller than any other computer built so far. Furthermore, particular mathematical computations have been demonstrated to work on a DNA computer.
DNA computing does not provide any new capabilities from the standpoint of computability theory, the study of which problems are computationally solvable using different models of computation.
For example,
if the space required for the solution of a problem grows exponentially with the size of the problem (EXPSPACE problems) on von Neumann machines, it still grows exponentially with the size of the problem on DNA machines.
For very large EXPSPACE problems, the amount of DNA required is too large to be practical.