双重的力量（在自组装）：它不是那么时髦是广场
The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square
摘要：
在本文中，我们定义了双重抽象瓦片组装模型（DaTAM），这是一个轻微的扩展抽象瓦片组装模型（aTAM），不仅允许标准的正方形瓦片，但也“双重”瓦片，这是由两个正方形瓦片连接预形成的矩形。我们表明，添加双链允许在温度1下自组装系统的强大行为，这意味着系统排除了瓦片合作结合的要求（即，如果要附着，则要求瓷砖必须能够结合到现有组件中的至少2个瓷砖上）。合作绑定是需要在标准的aTAM图灵通用计算和有效的自组装形状，但我们表明，在DaTAM这些行为实际上可以表现出在温度1。然后，我们表明，DaTAM不提供渐近改进的aTAM在其能力，有效地建立薄矩形。最后，我们给出了一系列的结果，证明了温度-2 aTAM和温度-1 DaTAM具有互斥的权力。也就是说，每一个都能够自我组装形状，而另一个不能，每一个都有系统，而另一个不能模拟。除了纯理论上的兴趣，这些结果具有实际的动机，因为双重体已经被证明在基于DNA的瓦片的实验室实现中是有用的。
英文摘要：
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles pre-formed by the joining of two square tiles. We show that the addition of duples allows for powerful behaviors of self-assembling systems at temperature 1, meaning systems which exclude the requirement of cooperative binding by tiles (i.e., the requirement that a tile must be able to bind to at least 2 tiles in an existing assembly if it is to attach). Cooperative binding is conjectured to be required in the standard aTAM for Turing universal computation and the efficient self-assembly of shapes, but we show that in the DaTAM these behaviors can in fact be exhibited at temperature 1. We then show that the DaTAM doesn't provide asymptotic improvements over the aTAM in its ability to efficiently build thin rectangles. Finally, we present a series of results which prove that the temperature-2 aTAM and temperature-1 DaTAM have mutually exclusive powers. That is, each is able to self-assemble shapes that the other can't, and each has systems which cannot be simulated by the other. Beyond being of purely theoretical interest, these results have practical motivation as duples have already proven to be useful in laboratory implementations of DNA-based tiles.
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