具有吸引力和排斥力的通用形状复制器
Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces
摘要：
我们展示了如何在具有吸引力和排斥力的自组装系统中设计一个通用的形状复制器。更确切地说，我们表明，有一个通用的一组恒定大小的对象，当添加到任何未知的无孔polyomino形状，产生无限数量的副本的形状（加上恒定大小的垃圾对象）。使用恒定数量的预处理自组装步骤，可以很容易地从恒定数量的单个瓦片类型构建恒定大小的对象。我们的构造使用了瓷砖自组装的良好研究的双手组装模型（2 HAM），在简单的模型中，胶水只与相同的胶水相互作用，允许胶水强度为正（吸引力）或负（排斥力），以及恒定的温度（部件保持在一起所需的胶水强度）。我们还要求给定的形状在其表面上具有指定的胶水类型，并且特征尺寸（非关联边之间的最小距离）由常数限制。形状复制必然需要一个自组装模型，其中部分可以连接和分离，这种构造是第一个使用负/排斥胶的自然模型（之前也研究过其他问题，如燃料效率计算）这样做;以前的复制构造需要更强大的全局操作，如“酶”破坏瓷砖类型的子集。
英文摘要：
We show how to design a universal shape replicator in a self-assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown hole-free polyomino shape, produces an unbounded number of copies of that shape (plus constant-size garbage objects). The constant-size objects can be easily constructed from a constant number of individual tile types using a constant number of preprocessing self-assembly steps. Our construction uses the well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the simple model where glues interact only with identical glues, allowing glue strengths that are either positive (attractive) or negative (repulsive), and constant temperature (required glue strength for parts to hold together). We also require that the given shape has specified glue types on its surface, and that the feature size (smallest distance between nonincident edges) is bounded below by a constant. Shape replication necessarily requires a self-assembly model where parts can both attach and detach, and this construction is the first to do so using the natural model of negative/repulsive glues (also studied before for other problems such as fuel-efficient computation); previous replication constructions require more powerful global operations such as an "enzyme" that destroys a subset of the tile types.
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