不可逆自组装中的负相互作用
Negative Interactions in Irreversible Self-Assembly
摘要：
本文探讨了否定词的使用（即，排斥）相互作用的抽象瓦片组装模型定义的Winfree。温弗里在他的博士学位中假设负相互作用在物理上是合理的。Reif，Sahu和Yin在可逆依恋操作的背景下探索了它们的力量。我们探索了不可逆依恋的负面互动的力量，我们得到了两个主要结果。我们的第一个结果是一个不可能性定理：在t步组装之后，Omega（t）瓷砖将永远绑定到一个组件上，无法分离。因此，负的胶强度不能提供无限的力量来重复使用瓷砖。我们的第二个结果是肯定的：我们构造了一组瓦片，它可以模拟一个具有空间约束s和时间约束t的图灵机，同时确保没有中间组件增长超过O（s），而不是标准图灵机模拟瓦片所要求的O（s * t）。
英文摘要：
This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles.
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