利用排斥力实现等尺度下的分子自组装
Self-Assembly of Shapes at Constant Scale using Repulsive Forces
摘要：
形状的算法自组装已被认为是在几个模型的自组装。对于\emph{shape construction}问题，我们考虑了一个扩展版本的双手瓦片组装模型（2 HAM），其中包含正（吸引）和负（排斥）的相互作用。因此，组件的部分可能变得不稳定并分离。在该模型中，我们利用节能计算来执行图灵机模拟来构建形状。在本文中，我们将展示如何使用渐进最优数量的不同瓷砖类型（基于形状的柯尔莫哥洛夫复杂性）构造任意形状。我们在这个简单的模型中以$O(1)$比例因子实现了这一点，而以前所有具有次线性比例因子的结果都利用了强大的自组装模型，其中包含分级，瓷砖删除，化学反应网络和瓷砖激活/失活等功能。此外，我们的结果中的计算和构造只创建了常量大小的垃圾程序集，作为组装形状的副产品。
英文摘要：
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains positive (attractive) and negative (repulsive) interactions. As a result, portions of an assembly can become unstable and detach. In this model, we utilize fuel-efficient computation to perform Turing machine simulations for the construction of the shape. In this paper, we show how an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (based on the shape's Kolmogorov complexity). We achieve this at $O(1)$ scale factor in this straightforward model, whereas all previous results with sublinear scale factors utilize powerful self-assembly models containing features such as staging, tile deletion, chemical reaction networks, and tile activation/deactivation. Furthermore, the computation and construction in our result only creates constant-size garbage assemblies as a byproduct of assembling the shape.
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