| Experiments have demonstrated that DNA molecules can compute like a machine to solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical reactions, DNA computation suffers from errors, which are its main limitation. The abstract and kinetic Tile Assembly Models are now commonly used to simulate real DNA computing experiments, and to look for new methods to advance the accuracy of DNA-based computation. One means of controlling errors is through proofreading tile sets. Several such tile sets have been proposed in the literature, such as Chen and Goel's snaked proofreading tile sets, the 2-way and 3-way overlay tile sets of Reif et al., and Rothemund and Cook's n-way overlay tile sets.;In the second part of this thesis, we focus on a different error mechanism, namely, errors caused by imperfect or malformed tiles. We propose a model of malformed tiles, and consider the performance of various proofreading tile sets in the presence of malformed tiles. Our simulation results show that the Reif et al. 3-way overlay tile sets are able to best deal with malformed tiles. During the simulations, we observed that snaked proofreading tile sets always have trouble completing whole patterns when malformed tiles are present. We instead propose two modified snaked proofreading constructions, and verify through both simulations and analysis that the two modified constructions have much better performances.;In the first part of this thesis, we analyze the performance of the Rothemund-Cook n-way overlay tile sets. We prove that the n-way overlay tile set contains n2+3n+4 rule tiles. Simulation results show that these tile sets clearly perform better than tile sets without any error-control mechanism, and the performance improves as n increases. It is also proved that the error rates in assemblies formed by the 1-way and 2-way tile sets are O(epsilon 2), where epsilon is the error rate in assemblies without any error correction. |
