On improving the expressive power of chemical computation

Abstract

Traditional CMOS computers are Turing complete information processing systems. They can compute any function that can be described algorithmically. In the past, the computing speed of such systems has been constantly improved. However, for various technological reasons this trends is expected to stop, and alternative ways of computing are under investigation. The computational power of chemical systems has been investigated for quite some time. However, it is not clear what the computing capacity of such systems is. It has been studied how to construct a Turing complete chemical computer in the well-mixed chemical reactor setup. Liekens and Fernando (“Turing complete catalytic computers”, in: Advances in Artificial life, Springer, 2007, pp. 1202-1211) have suggested a systematic way to investigate the chemical completeness issue. Their main finding was that chemical computers are Turing complete in principle. However, spontaneous errors in computation can occur. The frequency of these errors defines the fail rate. In this study, the aim is to understand how the effects of diffusion (e.g. speed of mixing) and the dimensionality of the system influence the fail rate. This is done by performing Monte Carlo simulations. The main conclusions are: The effects of diffusion are indeed extremely important. Finite mixing (low diffusion constant) leads to higher fail rates. It is possible to improve the accuracy of the computer (lower the fail rate) by optimizing the reaction system that implements the chemical computer.