| Self-assembly is an emerging computing paradigm potentially useful in fields that range from electronics and nanorobotics to biology. A promising approach for designing and building practical Self-assembly systems in the lab is to combine carefully designed DNA molecules [21, 22, 18].; In addition to all the practical problems to be solved in the lab, the design of Self-assembly systems seems to require to consider higher level issues. These considerations are analogous to designing and analyzing algorithms. Self-assembly can be thought of as a program running on a digital computer [12, 14, 20, 15, 16, 3, 4]. We can try to optimize Self-assembly systems, as we can try to optimize conventional programs. Another aspect to be considered is robustness. Lab experiments suggest that error detection and/or correction mechanisms are needed.; We show that the problem of optimizing for space is NP-complete in the Tile Assembly model. We describe how to analyze the running time for some families of Self-assembly systems, such as partial-order systems. We conjecture that optimizing for time by selecting concentrations functions is #P-hard and we show approximation techniques that allow efficient optimizations. We define invadable systems in the Tile assembly model, that allow error correction based on strand invasion. We show an efficient counter construction that solves an open problem formulated in [3]. We describe progress towards finding an optimal size counter. We describe the mixers systems model of Self-assembly, which is based on differential equations. The mixer systems is a generalization of Reaction-networks, introduced by Martin Feinberg [9]. We prove basic properties of this new model related to the range of their solutions and about the existence of nontrivial polynomial conservation laws. |
