温度模糊自组装的强容错性
Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature
摘要：
我们考虑了纳米级算法自组装的容错问题。我们采用Winfree的抽象瓦片组装模型（aTAM）的变体，双手aTAM，其中方形“瓦片”--一种从DNA构建的分子模型，用于工程自组装纳米结构--根据不同强度的特定结合位点聚集，并且其中瓦片的大聚集体可以彼此附着，与种子aTAM相反，其中瓦片一次一个地聚集成单个专门指定的“种子”组件。我们专注于基于瓦片的自组装中错误的主要原因：由于“弱”强度-1键导致的非预期增长，如果允许持续存在，可能会通过随后的相邻瓦片连接来稳定，因为现在至少需要能量2来分裂所得的组装;即，错误的组装在温度2下是稳定的。我们研究了一个常见的自组装基准问题，即组装一个n × n平方米使用O（log n）独特的瓷砖类型，根据双手模型的自组装。我们的主要结果实现了一个更强大的容错比以前实现的概念。允许任意强度-1增长（即，温度是“模糊的”，并且可以在任意长时间内从2漂移到1）;然而，任何在温度2下充分生长以变得稳定的组件都保证在温度2下组装成正确的N × N正方形的最终组件。换句话说，由于连接不充分而导致的错误，这是在早期容错论文中研究的错误的原因，在我们的主要结构中被绝对防止，而不是像以前的容错研究那样，只有高概率和足够小的结构。
英文摘要：
We consider the problem of fault-tolerance in nanoscale algorithmic self-assembly. We employ a variant of Winfree's abstract Tile Assembly Model (aTAM), the two-handed aTAM, in which square "tiles" -- a model of molecules constructed from DNA for the purpose of engineering self-assembled nanostructures -- aggregate according to specific binding sites of varying strengths, and in which large aggregations of tiles may attach to each other, in contrast to the seeded aTAM, in which tiles aggregate one at a time to a single specially-designated "seed" assembly. We focus on a major cause of errors in tile-based self-assembly: that of unintended growth due to "weak" strength-1 bonds, which if allowed to persist, may be stabilized by subsequent attachment of neighboring tiles in the sense that at least energy 2 is now required to break apart the resulting assembly; i.e., the errant assembly is stable at temperature 2. We study a common self-assembly benchmark problem, that of assembling an n x n square using O(log n) unique tile types, under the two-handed model of self-assembly. Our main result achieves a much stronger notion of fault-tolerance than those achieved previously. Arbitrary strength-1 growth is allowed (i.e., the temperature is "fuzzy" and may drift from 2 to 1 for arbitrarily long); however, any assembly that grows sufficiently to become stable at temperature 2 is guaranteed to assemble at temperature 2 into the correct final assembly of an n x n square. In other words, errors due to insufficient attachment, which is the cause of errors studied in earlier papers on fault-tolerance, are prevented absolutely in our main construction, rather than only with high probability and for sufficiently small structures, as in previous fault-tolerance studies.
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