Self-correcting Self-assembly: Growth Models and the Hammersley Process

In many respects, the current state of DNA-based computing resembles the state of standard, electronic computing a half century ago: a fascinating prospect is slow to develop owing to inflexible interfaces and unacceptably low reliability of the computational processes. We concentrate in this paper on the latter aspect, specifically addressing the interplay between the reliability and speed of DNA computing. While DNA-based computational devices are known to be extremely energy efficient, their reliability is seen as the greatest obstacle to becoming a viable computing environment. As DNA based computing becomes more fully developed, the speed of self assembly will become a crucial factor; but as of now, little is known concerning the fundamental question of computation times. We emphasize the intrinsic connection between the two problems of reliability and speed, because of the unavoidable trade-off that exists between them. A clear understanding of the limitations of self-assembly reliability and speed, specifically that of DNA-based computing, and the interplay between these properties, will be paramount in determining the full potential of the paradigm. In our past work, which is briefly reviewed below, we analyzed, for a given function, the time required to determine its value on given inputs, and therefore, established theoretical limits on the performance of DNA-based computers. In the simplest instance, the analysis of computation times has surprising connections with interacting particle systems and variational problems, as shown in [1], and as further developed here. The critical new dimension of this paper lies in (a) a novel approach to dramatic improvements in the reliability of computations and (b) in the analysis of the inevitable performance losses of reliable computations.