高温分级自组装系统的模拟能力与局限性
The Simulation Powers and Limitations of Higher Temperature Hierarchical Self-Assembly Systems
摘要：
在本文中，我们扩展了现有的结果模拟和内在的普遍性在一个模型的瓷砖为基础的自组装。也就是说，我们在双手组装模型（2HAM）中工作，这是一种自组装模型，其中组件由允许组合的正方形瓦片形成，沿着它们的边缘使用胶水，单独地或作为分层方式中的任意大组件对，并且我们探索这些系统在模拟系统具有较高的“温度”参数时相互模拟的能力，这是一个系统范围的阈值，规定了在两个组件之间必须形成多少胶粘结以允许它们结合。先前已经表明，具有较低温度的系统不能模拟具有较高温度的任意系统，并且在某些较高温度下的系统可以模拟那些在特定较低温度下的系统，从而创建无限组无限层次的2HAM系统，其中每个层次内的模拟能力严格增加。这些先前的结果依赖于两种不同的模拟定义，一种（强模拟）似乎比另一种（标准模拟）更具限制性，但以前没有被证明是不同的。在这里，我们证明了它们之间的区别，首先充分表征了一组温度对，使高温系统本质上是通用的较低的温度系统（即一个瓷砖设置在较高的温度可以模拟任何在较低的）使用强模拟。这包括温度向下模拟的第一个不可能结果。然后，我们表明，较低的温度系统，不能模拟较高的温度系统使用强定义，实际上可以模拟使用标准定义，证明了不同类型的模拟之间的区别。
英文摘要：
In this paper, we extend existing results about simulation and intrinsic universality in a model of tile-based self-assembly. Namely, we work within the 2-Handed Assembly Model (2HAM), which is a model of self-assembly in which assemblies are formed by square tiles that are allowed to combine, using glues along their edges, individually or as pairs of arbitrarily large assemblies in a hierarchical manner, and we explore the abilities of these systems to simulate each other when the simulating systems have a higher "temperature" parameter, which is a system wide threshold dictating how many glue bonds must be formed between two assemblies to allow them to combine. It has previously been shown that systems with lower temperatures cannot simulate arbitrary systems with higher temperatures, and also that systems at some higher temperatures can simulate those at particular lower temperatures, creating an infinite set of infinite hierarchies of 2HAM systems with strictly increasing simulation power within each hierarchy. These previous results relied on two different definitions of simulation, one (strong simulation) seemingly more restrictive than the other (standard simulation), but which have previously not been proven to be distinct. Here we prove distinctions between them by first fully characterizing the set of pairs of temperatures such that the high temperature systems are intrinsically universal for the lower temperature systems (i.e. one tile set at the higher temperature can simulate any at the lower) using strong simulation. This includes the first impossibility result for simulation downward in temperature. We then show that lower temperature systems which cannot be simulated by higher temperature systems using the strong definition, can in fact be simulated using the standard definition, proving the distinction between the types of simulation.
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