Abstract: Recently, many researchers demonstrate that two-dimensional self-assembly model has universal computational power, and DNA computing by self-assembly is proved to be scalable. With the development of molecular biology techniques,DNA computing by self-assembly has promising prospects, and it has more innovations and applications in nano-science, optimization calculation, cryptography, medicine and other areas. This paper gave more comprehensive introductions to the current status of the research, molecular structure, mathematical models, complexity and error analysis of DNA computing by self-assembly. Also, the problems to be studied and prospect of DNA computing by self-assembly were analyzed.

Key words: Self-assembly model, Universal computational power, DNA computing by self-assembly, Scalable, Nano-science, Complexity, Error analysis