用于瓦片自组装的异步信号传递：燃料效率计算和瓦片的高效组装
Asynchronous Signal Passing for Tile Self-Assembly: Fuel Efficient Computation and Efficient Assembly of Shapes
摘要：
在本文中，我们展示了瓦自组装模型的基础上，可以动态地改变状态的活性胶的权力。基于Padilla、Liu和Seeman的异步模型，我们制定了信号传递瓦片组装模型（STAM），允许以任何顺序发生打开或关闭胶水、连接新瓦片或拆分组件的任何动作。在这个高度概括的模型中，我们提供了三个新的解决方案，瓷砖自组装的问题，已经解决了抽象的瓷砖组装模型及其变体，表明信号传递瓷砖允许跨多个复杂性指标的大幅改善。我们的第一个结果利用递归组装过程来实现瓷砖型高效组装的线性结构，使用可证明更少的瓷砖类型比什么是可能的标准瓷砖组装模型。我们的第二个系统的信号传递瓷砖模拟任何图灵机与高燃料效率，通过使用一个恒定的瓷砖数量，每个计算步骤。我们的第三个系统组装离散的谢尔宾斯基三角形，表明这种模式可以严格自组装的STAM内。这一结果是特别感兴趣的，因为它是已知的，这种模式不能自组装在一些研究良好的瓷砖自组装模型。值得注意的是，我们所有的结构都处于温度1，进一步证明了信号传递赋予了绕过标准瓦片组件模型中的许多限制的能力。
英文摘要：
In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla, Liu, and Seeman to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
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