这是一个艰难的纳米世界：在瓷砖组装中，合作并不比竞争更强大
It's a Tough Nanoworld: in Tile Assembly, Cooperation is not (strictly) more Powerful than Competition
摘要：
我们提出了一个严格的分离类之间的“失配自由”自组装系统和一般的aTAM系统。无失配系统是指并发生长的部件必须始终彼此一致的系统。瓦片自组装是晶体生长形成的模型，其中大量颗粒同时并选择性地彼此粘附，形成复杂的形状和结构。它在纳米技术中很有用，更普遍地说，它在理解这些在自然系统中无处不在的过程中很有用。局部组装过程的另一个已知的改变模型能力的属性是两个瓦片之间的合作以连接另一个瓦片。我们表明，分歧（不匹配）和合作是不可比拟的：既不能用来模拟另一个。错配是硬属性的事实是特别令人惊讶的，因为没有已知的，明确的构造的计算设备在瓦片组装使用错配，除了最近的构造的本质上通用的tiltrons，即能够模拟任何其他tiltrons直到重新缩放的tiltrons。这项工作展示了如何使用内在的普遍性，以系统的方式，突出不同的瓷砖组装功能的本质。此外，即使是最新的实验实现也没有使用竞争，鉴于我们的结果，这表明DNA自组装背后的大部分自然现象仍有待实验理解。
英文摘要：
We present a strict separation between the class of "mismatch free" self-assembly systems and general aTAM systems. Mismatch free systems are those systems in which concurrently grown parts must always agree with each other. Tile self-assembly is a model of the formation of crystal growth, in which a large number of particles concurrently and selectively stick to each other, forming complex shapes and structures. It is useful in nanotechnologies, and more generally in the understanding of these processes, ubiquitous in natural systems. The other property of the local assembly process known to change the power of the model is cooperation between two tiles to attach another. We show that disagreement (mismatches) and cooperation are incomparable: neither can be used to simulate the other one. The fact that mismatches are a hard property is especially surprising, since no known, explicit construction of a computational device in tile assembly uses mismatches, except for the recent construction of an intrinsically universal tileset, i.e. a tileset capable of simulating any other tileset up to rescaling. This work shows how to use intrinsic universality in a systematic way to highlight the essence of different features of tile assembly. Moreover, even the most recent experimental realizations do not use competition, which, in view of our results, suggests that a large part of the natural phenomena behind DNA self-assembly remains to be understood experimentally.
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