尺寸可分离的瓦片自组装：温度为1的无错配系统的紧边界
Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free Systems
摘要：
我们介绍了瓷砖自组装系统的一个新的属性，我们称之为大小分离。一个系统是大小可分的，如果每个终端组件是一个常数因子大于任何中间组件。尺寸可分离性是由使用凝胶电泳或其他基于质量的过滤技术从各种不完整的“垃圾”组件中过滤完成的组件的实际问题激发的。在这里，我们证明，任何系统没有合作的键合组装一个独特的不匹配的终端组件可以用来构建一个尺寸可分离的系统唯一组装相同的形状。证明实现了尺寸可分离系统的最佳比例因子和温度。作为证明的一部分，我们得到了两个结果的独立利益的失配温度-1双手系统。
英文摘要：
We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical problem of filtering completed assemblies from a variety of incomplete "garbage" assemblies using gel electrophoresis or other mass-based filtering techniques. Here we prove that any system without cooperative bonding assembling a unique mismatch-free terminal assembly can be used to construct a size-separable system uniquely assembling the same shape. The proof achieves optimal scale factor and temperature for the size-separable system. As part of the proof, we obtain two results of independent interest on mismatch-free temperature-1 two-handed systems.
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