Complexity Issues

4.13 Summary

In this chapter we have emphasized the rôle that complexity considerations are likely to play in the identification of “killer applications” for DNA computation. We have examined how time complexities have been estimated within the literature. We have shown that these are often likely to be inadequate from a realistic point of view. In particular, many authors implicitly assume that arbitrarily large numbers of laboratory assistants or robotic arms are available for the mechanical handling of tubes of DNA. This has often led to serious underestimates of the resources required to complete a computation.

We have proposed a so-called strong model of DNA computation, which we believe allows realistic assessment of the time complexities of algorithms within it. This model, if the splice operation is trivially included, not only provides realistic estimates of time complexities, but is also Turing-complete. We have also demonstrated how existing models of computation (Boolean circuits and the P-RAM) may be effectively simulated in DNA.

We believe that success in the search for “killer applications” is the only means by which there will be sustained practical interest in DNA computation. Success is only a likely outcome if DNA computations can be described that will require computational resources of similar magnitude to those required by conventional solutions. If, for example, we were to establish polylogarithmic time computations using only a polynomial volume of DNA, then this would be one scenario in which “killer applications” might well ensue. In this case, we might imagine that the vast potential for parallelisation may finally be effectively harnessed.