非合作瓦片装配模型本质上不具有通用性，也不能进行有界图灵机仿真
The non-cooperative tile assembly model is not intrinsically universal or capable of bounded Turing machine simulation
摘要：
算法自组装领域关注纳米级自组装分子系统的计算能力和表达能力。在研究得很好的合作，或温度2，抽象瓦片组装模型，它是已知的，有一个瓦片集模拟任何图灵机和一个固有的通用瓦片集，模拟模型的任何实例的形状和动力学，直到空间重新缩放。这一直是一个悬而未决的问题，是否似乎更简单的非合作，或温度1，模型是能够这样的行为。在这里，我们表明，这是不是这样的情况下，通过显示，有没有瓷砖集的非合作模型，这是内在的普遍性，也没有一个能够有界的图灵机模拟在一个有界的区域内的平面。虽然非合作模型在直觉上似乎缺乏合作模型的复杂性和力量，但如何证明这一点并不明显。原因之一是，很少有工具来分析平面上复杂路径的结构。本文件提供了一些这样的工具。第二个原因是，几乎每一个明显的和小的概括模型（例如，允许错误，3D，非正方形瓷砖，瓷砖上的信号/电线，互相排斥的瓷砖，并行同步增长）赋予它巨大的计算能力，有时模拟，权力。我们的主要结果表明，所有这些概括证明增加计算和/或模拟能力。我们的结果适用于确定性和非确定性的非合作系统。我们的第一个主要结果与以下事实形成鲜明对比：对于合作瓦片组件模型和3D非合作瓦片组件，存在各自的固有通用瓦片集。我们的第二个主要结果给出了一个新的技术（减少模拟）证明在瓷砖组装计算的负面结果。
英文摘要：
The field of algorithmic self-assembly is concerned with the computational and expressive power of nanoscale self-assembling molecular systems. In the well-studied cooperative, or temperature 2, abstract tile assembly model it is known that there is a tile set to simulate any Turing machine and an intrinsically universal tile set that simulates the shapes and dynamics of any instance of the model, up to spatial rescaling. It has been an open question as to whether the seemingly simpler noncooperative, or temperature 1, model is capable of such behaviour. Here we show that this is not the case, by showing that there is no tile set in the noncooperative model that is intrinsically universal, nor one capable of time-bounded Turing machine simulation within a bounded region of the plane. Although the noncooperative model intuitively seems to lack the complexity and power of the cooperative model it was not obvious how to prove this. One reason is that there have been few tools to analyse the structure of complicated paths in the plane. This paper provides a number of such tools. A second reason is that almost every obvious and small generalisation to the model (e.g. allowing error, 3D, non-square tiles, signals/wires on tiles, tiles that repel each other, parallel synchronous growth) endows it with great computational, and sometimes simulation, power. Our main results show that all of these generalisations provably increase computational and/or simulation power. Our results hold for both deterministic and nondeterministic noncooperative systems. Our first main result stands in stark contrast with the fact that for both the cooperative tile assembly model, and for 3D noncooperative tile assembly, there are respective intrinsically universal tilesets. Our second main result gives a new technique (reduction to simulation) for proving negative results about computation in tile assembly.
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