DNA walker circuits: computational potential, design, and verification

Abstract. Unlike their traditional, silicon counterparts, DNA computers have natural interfaces with both chemical and biological systems. These can be used for a number of applications, including the precise arrangement of matter at the nanoscale and the creation of smart biosensors. Like silicon circuits, DNA strand displacement systems (DSD) can evaluate non-trivial functions. However, these systems can be slow and are susceptible to errors. It has been suggested that localised hybridization reactions could overcome some of these challenges. Localised reactions occur in DNA ‘walker ’ systems which were recently shown to be capable of navigating a programmable track tethered to an origami tile. We investigate the computational potential of these systems for evaluating Boolean functions. DNA walkers, like DSDs, are also susceptible to errors. We develop a discrete stochastic model of DNA walker ‘circuits ’ based on experimental data, and demonstrate the merit of using probabilistic model checking techniques to analyse their reliability, performance and correctness.

Forming tile shapes with simple robots

Motivated by the problem of manipulating nanoscale materials, we investigate the problem of reconfiguring a set of tiles into certain shapes by robots with limited computational capabilities. As a first step towards developing a general framework for these problems, we consider the problem of rearranging a connected set of hexagonal tiles by a single deterministic finite automaton. After investigating some limitations of a single-robot system, we show that a feasible approach to build a particular shape is to first rearrange the tiles into an intermediate structure by performing very simple tile movements. We introduce three types of such intermediate structures, each having certain advantages and disadvantages. Each of these structures can be built in asymptotically optimal $O(n^2)$ rounds, where $n$ is the number of tiles. As a proof of concept, we give an algorithm for reconfiguring a set of tiles into a triangle through one of the intermediate structures