Theoretical and Experimental DNA Computation (Natural ...

4
Complexity Issues
“Out of intense complexities intense simplicities emerge.”
– Sir Winston Churchill.
In this chapter we present an analysis of the complexity and viability of DNA
computations. Such analysis has, in part, been motivated by the search for
so-called “killer applications”: applications of this mode of computation that
would establish its superiority within a certain domain. An assured future for
DNA computation can only be established through the the discovery of such
applications. We introduce our framework for the analysis of DNA algorithms,
and argue that existing analyses are flawed and unrealistic. In particular, we
argue that computations that are assumed to run in polylogarithmic time
actually take polynomial time to realize in the laboratory. We develop further
our analysis to motivate the strong model of DNA computation, and analyze
existing algorithms within it. We argue that our strong model may provide
more realistic estimates of the resources required by DNA algorithms. We
show how existing models of computation (Boolean circuit and P-RAM) may
be effectively simulated using DNA, and give a general framework for the
translation of high-level algorithms down to the level of operations on DNA.
4.1 Introduction
Following the initial promise and enthusiastic response to Adleman’s seminal
work [3] in DNA computation, progress towards the realization of worthwhile
computations in the laboratory became stalled. One reason for this is that the
computational paradigm employed by Adleman, and generalized by the theoretical
work of others [12, 98, 128], relies upon filtering techniques to isolate
solutions to a problem from an exponentially sized initial solution of DNA.
This volume arises because all possible candidate solutions have to be encoded
in the initial solution. As Hartmanis points out in [76], the consequence